As a human being he had to grow and learn just as we all do, but what he learned was the Old Testament.
It is interesting that you say this.
I sometimes see people referencing a statement by Jesus, say about Jonah or about Noah, and saying that since Jesus was omniscient this shows that the OT story is literally true. However, if Jesus was human and had to learn just as everybody else, then that is not persuasive reasoning. If he was omniscient, then there was no need to learn.
By the way, I agree that the gospel stories require that Jesus was human and not omniscient during his earthly lifetime. Otherwise he could not have been subject to temptation. It seems to me that the gospel story depends on this.