Sure, God COULD do anything, but the question is “Did it really happen?”
This is the same argument the Mormons use regarding Joseph Smith: “Don’t you believe God could have spoken to Joseph Smith?” And when you say “I cannot limit an omnipotent God.” They say “Well there you go.” As though possibility is proof. It isn’t.
It all goes back to Mary being defined as "Theotokos" ("God bearer") and the fear that early and medieval Christians had about Jesus as the "judge". He was a harsh, threatening, judgmental, kingly figure that scared them - how could one possibly talk to Jesus? So they turn to the soft, feminine, non-threatening, mother figure of Mary. Combine that psychology with a bunch of pagans who are joining the "religion of the Empire" because its the thing to do - pagan people used to worshipping goddesses like Artemis and Aphrodite - and you can easily see where this whole Marian thing crept into the Church.
There's absolutely nothing in any of the writings of the early Church (say, pre-4th century, or so) about Mary. Nothing about her as anything other than the mother of the Lord, and showing her great respect and honor. But there's no prayers, nothing about prayers, no speaking of her as an intercessor, or an advocate, or anything else like that.
No, Marian doctrine doesn't seem to take hold and really get going until after Christianity becomes the religion of the Empire and all the pagans start joining in great numbers. The early church fathers writings don't indicate anything like what the later Marian doctrines contain.
Therefore the Marian stuff seems to be a later invention of the Church itself, with no basis in history, Scripture or early tradition from the early Church fathers.