Yes, I usually come across them when reading the scriptures and referencing commentaries...Like when you are reading about the Pharisee and the publican praying at the hour of prayer at the temple. The commentaries on this will often reference background information and ancient sources about how they would stand and pray audibly with others around them all doing the same thing at the same time. I suppose it was much like the wailing wall is today.
That's a bit different from a corporate meeting in the synagogue. The temple compound was a huge area where they engage in individual prayer, hear teaching on the law, and offer sacrifices. Jesus also told his followers not to be like the hypocrites who loved to pray in the synagogues and on street corners. I am not sure that is an argument for everyone praying at the same time. They might have used synagogue buildings as places of private prayer, or some men in the synagogue could have taken turns making long prayers with an attention-seeking attitude to get praise from men rather than God.
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I think you will be able to find many ancient documents with a Google search "What ancient documents describe Jews in corporate prayer" You will have to be patient but some of the good documents will reference other sources and you should be able to discover the best sources from rabbinical writings, the Talmud, Josephus, etc.
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If you have anything specific, I would be interested in that. Just reading I Corinthians 14, Paul was concerned that prayer in a corporate setting also exhort others. Prayer is not exempt from 'let all things be done unto edifying.' If you pray in tongues how will others agree with it and say 'amen' if they do not know what you are saying? If everyone prays in tongues in English or Greek or whatever, we cannot hear each other and be edified by the prayer because we are all praying at once.
I was raised in A/G churches where I didn't hear the pray-at-the-same-time thing. I don't remember that at the independent Full Gospel church I went to, either. (I moved quite a bit.) Also, the practice at the A/Gs wasn't to all pray in tongues at once. Rather, one person would speak in tongues and the rest would interpret. An exception might be when someone is empowered by the Holy Spirit to speak in tongues for the first time at the laying on of hands. But, otherwise, I don't remember en masse speaking in tongues or tongues without interpretation, and one A/G church that had a Bible College affiliated with it taught that tongues in church needed to be interpreted. Probably some time over that, the General Overseer of the denomination went in the opposite direction from that however, leading everyone in a denominational assembly in en masse speaking in tongues, I read later.
Later, I heard some of the Pentecostals churches in the Southeast, where the congregation prays all at the same time, even in English, and I've heard that with Charismatics overseas. I don't think it fits with the themes taught in I Corinthians 14 since you can't make out what people are saying and be edified. I don't care for the practice of everyone singing something different at the same time, either. If we'd take turns and listen, we might be edified.
Given the overall themes of the passage, I am inclined to take 'let him keep silent in the church and let him speak to himself and to God' to refer to speaking to himself and to God as something that can take place out of the assembly. If you are standing there mumbling in tongues, unbelievers might still say 'ye are mad.'
Whether it is references to rules of liturgy or what the early church corporate prayer looked and sounded like I think you will find lots of evidence that they spoke, and not that they THOUGHT prayers.
Be that as it may, that doesn't mean that it was the practice of the early church for individuals in church to all pray at the same time--- so they couldn't hear each other and be edified--- rather than to take turns.
I have always felt the need to pray with my words and not just my thoughts since I was a new Christian. I think it was because I did not see evidence in scripture that Thinking prayers was a biblical concept. But also I just felt more faith for speaking prayers.
I prefer to pray out loud, also, if it is just me. But listening to someone else's prayer and saying 'amen' counts as well.
Some people think this prayer might have been silent.
Nehemiah 2
4 Then the king said unto me, For what dost thou make request? So I prayed to the God of heaven.
5 And I said unto the king, If it please the king, and if thy servant have found favour in thy sight, that thou wouldest send me unto Judah, unto the city of my fathers' sepulchres, that I may build it.