I'm acknowledging his truly human nature, that he was like us in every way except that he did not sin. He was truly the Son of God, but while on earth he was in the form of a human.
I don't think that a human being can be omniscient, indeed we can only contain so much information in our brain.
“Men of Israel, hear these words: Jesus of Nazareth, a man attested to you by God with mighty works and wonders and signs that God did through him in your midst, as you yourselves know—" Acts 2:22 (ESV)
God performed the works through Jesus, hence he was filled with the Holy Spirit who led him and it was from there he gained the powers to heal and prophesy.