After God kicked Adam out of the Garden;
Genesis 4:1 says;
And Adam knew Eve : and she conceived.....
Up to this time, there has been no mention of a wedding ceremony; and Cain is never called a bastard.
I have an opinion.
it goes like this;
the first time a male has sex with a female, he leaves off being a boy, leaves his Mother behind, becomes a man, and cleaves to his helpmate. That cleaving, is the marriage.
It can happen that the boy has sex too early in his life, and the cleaving does not take place.
In the Bible; the men were all older and most were well established before they went to obtain a wife. Furthermore, much later in history, the children of God were instructed NOT to take spouses from outside the Family.
Before the Flood, men routinely waited until after they were past 100 years old to sire children. Since there was no bith-control at that time, the implication is that the also waited that long before they took a "wife". The youngest on record is Cainan who sired Mahalaleel at 65. The oldest is Methuselah who sired Lamech at 187.... Except for Noah, who's boys were about 100years old as they came thru the Flood, Noah being 600ish. So now, Shem, Ham, and Japheth had only been "married" for about a year and change, when they began to repopulate the Earth.
The point is that these patriarchs were mature men, and well established, when they "took" wives. The tendency today is to rush our children into marriage, far too early. And parents do not take on their roles properly to prevent pre-marital sex.
So it's inevitable that children are born out of wedlock.
And no one can say that the parents of bastards should wed because obviously, those kids did not know what they were getting into. They did not have the sense to think it thru. Well, usually the boy does, but without a proper Biblical foundation, he just does whatever he wants; especially if he is not a Christian.
What has that got to do with it?
Well, go back and read what God has to say about it. and
Remember, that we allow our governments to indoctrinate our kids, in school, with; The Theory of Evolution, Big-Bang Theory, and ball-Earth theory,which combine to produce a Godless World were since there is no absolute morality, anything and everything is permissible.
What to do in your case, I cannot pretend to say, but one thing for sure I know; And this is NOT racist:
If the girl, and the boy, don't have the same skin color, the relationship is not likely to survive. If the girl is white and has any Christian values at all, but the boy hates Christianity, it will never work. Some of those Pagan and or Heathen religions are based very strongly on the mandate to "be fruitful and multiply", and they are not at all particular about what women they sow their seeds into. And they will never stop at just one woman. So if the boy is of one of those, and the girl is not, then there is no way I would enforce a marriage, and no way I would endorse giving his name to the offspring....... because he may just be between women.
In history; God told the Israelite men not to take a Foreign wife, because He said, they would lead the man to her religion, which thing God hated.
And every time we see an example of that in the Bible, it exactly comes true.
Furthermore, when Nehemia came to power, he forced all the Israelite men to cast off their foreign wives, and children of those wives.
I can sympathize with your plight, because My own, only son, a "good" boy as man counts good, has three children with a "wife" he has no certificate of marriage with. So those kids are all bastards by definition. Neither of the parents is a Christian, and neither is a Believer (obviously). But none are practicing Pagans either. And they both are white, with a strong moral upbringing. So NONE of this family has their names written in the Book of Life. They have been together for about 9 years, so we are still hoping and praying for them.
And as far as I'm concerned, they were wed, Biblically, when they "knew" eachother..... and all the kids have my last name....... because;
my genes are in them no matter what.
Consider this;
King David "took" the already "married" Bathsheba. Then conspired to have her husband killed. Not once but several times.
Yet it is from the line of David and Bathsheba,
that Jesus would eventually come.