Without your parenthetical, a lot of “marriages” happen without benefit of ceremony or commitment.
Marriage is a Biblically defined institution, and thus it’s a good idea to use that for the answer. The relevant scripture is Genesis 2:24, which implies a sexual union, though you could look at the first portion of this verse (”Therefore a man shall leave his father and his mother and hold fast to his wife...”) and interpret this ‘coming together’ as the act of marriage... the sexual part is indicated in most translations as coming afterward.
The Bible distinguishes between fornication and adultery, so it makes sense that the sexual act does not - in and of itself - constitute a marriage... Catholic teachings and traditions notwithstanding.
Regarding ceremonies: clearly these have changed over time, particularly since the State has stuck its nose in where it doesn’t belong. Again, because marriage is a God-defined institution, state involvement is irrelevant... though probably necessary for this day and age. In my opinion, a public declaration is important for the sake of the oaths.
While your history and scripture is extremely helpful, and your defense of their important quite agreeable. also agreeable is the important of anousement for the oath enforcement portion of marriage among many other perspectives you wisely brought to the table here.
I’m afraid however that your position and the position of the non-catholic faith is a bit unclear.
While it seems inferred that the catholic faith starts marriage at the first act of sex. As you illustrated that is not so clear in the bible as far as other christian faiths are concerned.
Because there are many possible answers in the ambquity I feel obliged to only ask you where you & your faith stand on this particular question, as I have asked of everyone else.
In Matthew 1:18 "...When his (Jesus') mother was espoused to Joseph, before they came together, she was found with child of the Holy Ghost." Some translations read "betrothed" rather than "espoused", but betrothal in that culture meant considerably more than betrothal/engagement today.
I do not know how long Mary and Joseph were in this espousal/pre-consumation state, but divorce was required to disolve the "marriage". See verse 19. Joseph had grounds, since he could have charged her with uncleanness BEFORE they had come together and consumated the marriage, after which he could not divorce her (Biblically).