What does our Father want?
In order to get a wife for Isaac, Abraham sent out a trusted servant. And the trusted servant prayed for God to bring him to the woman for Isaac and let him know she was the one God had chosen.
And it does not say anything about there being a ceremony or pronouncement.
But it was done as family, and with making sure with God. A mature and trustworthy and faithful and proven person made sure with God.
So, we can decoy ourselves with talking about outward actions and ceremony. But most of all we need to make sure with our Father, about who we belong with. And I would say that as Christians we are family with each other; so we want to have our mature example people and leaders sharing with us in finding out who we belong with and making sure with God. We need our example people to help us learn how to love in our marriage.
And Jesus says, "'Take My yoke upon you and learn from Me, for I am gentle and lowly in heart, and you will find rest for your souls.'" (Matthew 11:29) So, first we need to trust in Jesus and learn from Jesus who is our Groom . . . learn how Jesus has us loving in relating with Him as our Groom. And this loving is our example of how to be and share in marriage
So, if you are isolating yourselves and being immoral, I would say no this is not God's way of marriage. But if you as a couple are sharing with people who are Jesus' family, and if you are sharing with trustworthy leaders and other examples, in order to make sure and learn how to love, then keep on growing in love and discover how your relationship develops.
Do not be too concerned about what label to put on your sharing.
Most of all, I would say - - if you are growing in family and intimate sharing with each other, this is the best "part" of marriage . . . including how we are family and intimate with a variety of others who are Jesus love people (Ephesians 5:21, Ephesians 4:31-5:2, Ephesians 4:1-3, James 5:16, 1 Peter 5:3).
I am finding how I have a lady who is so good for me; she helps me to find out how to love, get corrected by God, and she can minister to me so I am alive in God's love so gentle and humble and quiet and pure. So, she is essential, like this, for me. So, if we do not get married, I still appreciate her and need her and would be glad to stay with her, if the LORD pleases. So, I would not marry someone who is not obviously helping you get real with God and get correction (Hebrews 12:4-17) to how Jesus wants us to love.
And your relationship needs to be shared as family with real Jesus people who you know are trustworthy and therefore you want them in on what you are doing

If you are really growing in God's love together, Christians will be able to see this, and they will feed on your example while helping you, too. But if you are isolating yourselves and only justifying what you are doing in secret, this is not how our Father has a marriage. But it may be how certain cultures and even legal systems have things.
But get into family sharing with real Jesus people and see what God satisfies you to do in agreement with good example leaders and mature Christian couples who you trust and enjoy and appreciate how their example feeds you how to love > "nor as being lords over those entrusted to you, but being examples to the flock." (1 Peter 5:3) They will know what to do with you

better than what you can do with each other
