I'll try to answer some of my own questions here as to why or how Jesus was able to do some of what he did with or without maybe knowing the full truth about the exodus, or other such kinds of things, etc.
He knew, or figured out, or deduced one single truth that was paramount for him maybe being able to do what he did, etc. And that was that if there was a highest God of all, one that was/always has been fully omniscient, and omnipotent, and all of that, etc, from the very beginning, etc, then it could not have been God in the OT, etc. But of course, he couldn't just come out and say this, like I can now, for some very, very obvious reasons back then, etc. But this was the truth that he ran across that might have been giving him the ability to do all of these kinds of things back then, etc.
But reasoning that there was such a most highest God as this, and claiming to be the only one living who fully knew Him, and represented Him, and could show Him, etc, he built a whole new entire teaching or theology around it. Which was that highest God as his true Father, and our Heavenly Father, and God in the OT as now God the Spirit, or the Holy Spirit now, after him, and Himself as the God-Man in that arrangement, etc. And his proof that he was correct, was his ability to do these kinds of things, or was in his having the (supernatural) power or authority to do these kinds of things, etc. And that his or this power could have come from his/our Heavenly Father God, or this Highest God, or God the Holy Spirit as his Father, etc, or maybe even a bit of both, etc.
But he was pretty much born with the ability to do these things, but didn't want it to become known publicly until his mother finally pushed him into it at the wedding in Cana of Galilee, at which point his mother thought his time, was already way, way, way overdue, etc.
But, anyway, his new found theology or belief may have been the source of him being able to do these kinds of things, etc, as the power or ability to do them might have come from there, etc, regardless of what his actual belief was about all of the other things, etc.
God Bless.