I've had dreams that have come true exactly as I've dreamt them. Déjà vu feels a little like that. I believe God gave me a few prophetic dreams (before I became born again with the Holy Spirit) as an answer to a question I asked Him or to prepare me emotionally for extremely difficult situations. Those dreams made me realize that everything is not as it was taught to me by society. Now, I am more aware of times when God is speaking to me so I don't experience déjà vu etc. as much.
One could say déjà vu are moments when the soul senses that there is something greater out there. If we are out of touch with God’s voice and not reborn with the Holy Spirit, we can easily dismiss them as an aberration of the brain or so-called “matrix” without realizing everything is not as we see.
Jesus Christ knew exactly what was going to happen (e.g. knowing which disciple would betray him and how all prophecy would be fulfilled far into the future) because his spirit was fully in touch with His Father in Heaven -- our Creator. As LOGOS, the Word of God made flesh, he was ‘there’ when the universe was created through God’s Word! I would even go as far as saying we have those moments thanks to Jesus Christ -- who is in touch with and wants to save every single human soul -- because he is the link between all souls and God. This is why he also said:
I am the way, the Truth and the Life. No one can come to the Father except by me (John 14:6)
-- He meant that literally and demonstrated it with all his miracles!
It's quite amazing when I am able to recognize, as I live my life, that a particular moment in time was portrayed exactly in a dream/vision. I am better able to adjust to the situation and adjust more quickly. In those moments, I remember to ask God what to do whereas before I might've forgotten to pray and seek His wisdom. These curious soul-pausing moments happen more when other people are involved... so maybe déjà vu are also times when God gives us an extra reminder that we can work FOR Him in some significant situation if we're being spiritually lacksadaisical!