If you are both committed to one and other, then Yahweh will know your hearts. He does not require a piece of paper to verify the marriage.
Taking a woman to be your wife is a commitment, and no amount of paper will enhance that commitment in front of Yahweh our Heavenly Father.
We are required by man's law to obtain a legal certificate.
Two virgins could come together as one and be fully committed. The certificate is a worldly thing.