Since our human bodies probably evolved over time and are due to natural processes (under God’s divine providence, of course), then we shouldn’t expect the creation account in Genesis to give a detailed biological explanation.
Rather, the point of Genesis is theological. The point, among other things, seems to be that man and woman are complementary, and that they need each other, and were made for relationship. Man is not an island.
So there is not objection, since God more than likely did not create man than woman in the exact word-for-word Genesis states. That doesn’t make Genesis untrue; we just have to read it with proper context in mind.
What I find more problematic are Paul’s words, in commentary on Genesis, when he says that “woman was made for man.”