If it is not a Christian belief, where does it come from, well lets look at the origin of these 'Mysteries'. It seems that many corruptions from Greek mythology and Hellenistic philosophy and other non Christian sources such as Gnosticism which came into the early church and this included the ancient 'Mysteries'.
So lets see what these were..
...The cults of the mystery religions were influenced uniformly by the ideas of the Greek philosophers. A few of them existed before the turn of the Era, but several more appeared at about the turn of the Era. They reached their height of popularity during the times of early Christianity. Christianity was born during a period of proliferation. Christianity itself in the beginning consisted of many cults that existed independently and had very diverse doctrines. Because of such diversity, it is debatable whether Gnosticism was just another cult of Christianity or whether it was a separate religion.
The following features were common to all mystery religions. Admission to the community was by a rite of initiation, a solemn consecration. The initiation was held in secret, which explains why they were called "mysteries."...
Esoteric Christianity: The Greek Mystery Religions and Their Impact on Christianity
Now the problem was that many Christians leaders were influenced or had picked up the pagan 'Mysteries' and mixed it with Christianity. Clement of Alexandria stated that 'what was taught in the Mysteries concerned the universe, and was the completion and perfection of all instruction; wherein things were seen as they were, and nature and her works were made known.'
Clement of Alexandria writings show that he was completely immersed in the pagan 'Myesteries' and are full of terminology taken directly from the language of the Pagan Mysteries. He writes of the Christian revelation as 'the holy Mysteries.' the ';divine secrets',... Clement further states 'I am become holy while I am being initiated.' Clement tells us that in early Christianity there were likewise Lesser Mysteries for beginners on the spiritual path and Greater Mysteries which were a secret higher knowledge, which led to full 'initiation.' The 'secret traditions of true Gnosis,' he explains, had been transmitted 'to a small number, by a succession of masters, and not in writing.'
So then we find the following connection...
"Alexandria was, in addition, one of the chief seats of that peculiar mixed pagan and Christian speculation known as Gnosticism. Basilides and Valentinus taught there. It is no matter of surprise, therefore, to find some of the Christians affected in turn by the scientific spirit. At an uncertain date, in the latter half of the second century, "a school of oral instruction" was founded. "
clement of alexandria
Note, it mixed pagan and Christian speculation, so a combining of paganism into Christianity
"The Mysteries demanded complete adherence to silence among its adherents."
'This demand was taken seriously in the Eleusinian Mysteries as failure to keep vows resulted in death. For this reason very little direct information exists concerning details of the Mysteries- the ritual, passwords, symbols and text."
"..More than five centuries before the arrival of Christianity, at Eleusis (a small town outside Athens) the people established the Eleusinian mysteries. There they reenacted the myth of Demeter's search and her reunion with her daughter Persephone. Every year two Eleusinian ceremonies were held: the Greater mysteries, in honor of Demeter and Kori, and the Lesser mysteries, in honor of Kori alone.
The Lesser mysteries were a preparation for the Greater ones. They were performed at Agrae on the river Ilissus (outside Athens) in the month of Anthesterion (February-March). Because of the oaths for secrecy we have sparse testimony of what exactly took place in the initiation ceremony. Something was recited, something was revealed, and acts were performed. Also, the initiates took an oath of secrecy before preparing for the Greater mysteries. The penalty for revealing the mysteries to outsiders was death. The initiates of the Lesser mysteries waited at least one year until they could participate in the Greater mysteries, which were held at Eleusis in the month of Boedromion (September-October). The Greater mysteries included baptism in the sea, three days of fasting, and the completion of the mysterious central rite. These acts completed the initiation, and the initiate was promised rewards in the life after death..."
Mithraism is an example of a "mystery religion" that flourished in the near east at that time. Mithraism took on the form of a mystery religion, with elaborate rights and ceremonies. It came into the ancient Roman world about 75 B.C. David Ulansey explains it is called such because " ..like the other ancient 'mystery religions,' such as the Eleusinian mysteries and the mysteries of Isis, the Mithraic cult maintained strict secrecy about its teachings and practices, revealing them only to initiates.
Did Christianity Steal From Mithraism? - Come Reason Ministries
The ancient mystery religions were secretive cults in the Greco=Roman world that had secret rites and initiation, and kept the 'mysteries' only to a select few. Here is what history tells us...
"Mystery religions, also known as mystery cults, were religious associations in the ancient world characterized by secrecy, initiation rites, and a focus on personal salvation. These cults provided individuals with religious experiences that were not available through the official public religions of the time. The term "mystery" derives from the Greek word "mysterion," which refers to secret knowledge or rites that were only revealed to initiates. "
https://www.britannica.com/topic/mystery-religion
So lets see what these were..
...The cults of the mystery religions were influenced uniformly by the ideas of the Greek philosophers. A few of them existed before the turn of the Era, but several more appeared at about the turn of the Era. They reached their height of popularity during the times of early Christianity. Christianity was born during a period of proliferation. Christianity itself in the beginning consisted of many cults that existed independently and had very diverse doctrines. Because of such diversity, it is debatable whether Gnosticism was just another cult of Christianity or whether it was a separate religion.
The following features were common to all mystery religions. Admission to the community was by a rite of initiation, a solemn consecration. The initiation was held in secret, which explains why they were called "mysteries."...
Esoteric Christianity: The Greek Mystery Religions and Their Impact on Christianity
Now the problem was that many Christians leaders were influenced or had picked up the pagan 'Mysteries' and mixed it with Christianity. Clement of Alexandria stated that 'what was taught in the Mysteries concerned the universe, and was the completion and perfection of all instruction; wherein things were seen as they were, and nature and her works were made known.'
Clement of Alexandria writings show that he was completely immersed in the pagan 'Myesteries' and are full of terminology taken directly from the language of the Pagan Mysteries. He writes of the Christian revelation as 'the holy Mysteries.' the ';divine secrets',... Clement further states 'I am become holy while I am being initiated.' Clement tells us that in early Christianity there were likewise Lesser Mysteries for beginners on the spiritual path and Greater Mysteries which were a secret higher knowledge, which led to full 'initiation.' The 'secret traditions of true Gnosis,' he explains, had been transmitted 'to a small number, by a succession of masters, and not in writing.'
So then we find the following connection...
"Alexandria was, in addition, one of the chief seats of that peculiar mixed pagan and Christian speculation known as Gnosticism. Basilides and Valentinus taught there. It is no matter of surprise, therefore, to find some of the Christians affected in turn by the scientific spirit. At an uncertain date, in the latter half of the second century, "a school of oral instruction" was founded. "
clement of alexandria
Note, it mixed pagan and Christian speculation, so a combining of paganism into Christianity
"The Mysteries demanded complete adherence to silence among its adherents."
'This demand was taken seriously in the Eleusinian Mysteries as failure to keep vows resulted in death. For this reason very little direct information exists concerning details of the Mysteries- the ritual, passwords, symbols and text."
"..More than five centuries before the arrival of Christianity, at Eleusis (a small town outside Athens) the people established the Eleusinian mysteries. There they reenacted the myth of Demeter's search and her reunion with her daughter Persephone. Every year two Eleusinian ceremonies were held: the Greater mysteries, in honor of Demeter and Kori, and the Lesser mysteries, in honor of Kori alone.
The Lesser mysteries were a preparation for the Greater ones. They were performed at Agrae on the river Ilissus (outside Athens) in the month of Anthesterion (February-March). Because of the oaths for secrecy we have sparse testimony of what exactly took place in the initiation ceremony. Something was recited, something was revealed, and acts were performed. Also, the initiates took an oath of secrecy before preparing for the Greater mysteries. The penalty for revealing the mysteries to outsiders was death. The initiates of the Lesser mysteries waited at least one year until they could participate in the Greater mysteries, which were held at Eleusis in the month of Boedromion (September-October). The Greater mysteries included baptism in the sea, three days of fasting, and the completion of the mysterious central rite. These acts completed the initiation, and the initiate was promised rewards in the life after death..."
Mithraism is an example of a "mystery religion" that flourished in the near east at that time. Mithraism took on the form of a mystery religion, with elaborate rights and ceremonies. It came into the ancient Roman world about 75 B.C. David Ulansey explains it is called such because " ..like the other ancient 'mystery religions,' such as the Eleusinian mysteries and the mysteries of Isis, the Mithraic cult maintained strict secrecy about its teachings and practices, revealing them only to initiates.
Did Christianity Steal From Mithraism? - Come Reason Ministries
The ancient mystery religions were secretive cults in the Greco=Roman world that had secret rites and initiation, and kept the 'mysteries' only to a select few. Here is what history tells us...
"Mystery religions, also known as mystery cults, were religious associations in the ancient world characterized by secrecy, initiation rites, and a focus on personal salvation. These cults provided individuals with religious experiences that were not available through the official public religions of the time. The term "mystery" derives from the Greek word "mysterion," which refers to secret knowledge or rites that were only revealed to initiates. "
https://www.britannica.com/topic/mystery-religion