Read what I said more carefully. Islam does not recognize Jesus the way Christians do. Nor do the Jews. And yet they marry freely. So you can get married without Jesus.
It does not matter in this case what God said to Adam and eve. Atheists and agnostics marry freely with no mention of God. Marriage is a civil liberty, done often by sanctioned government officials under no denomination in a courthouse. No one is fighting for the right to be married in a Catholic church. Marriage is not the property of religion. It exists outside of religion for millions already.