“Would this be similar to what I have heard taught in Evangelical churches for decades, that every human being has a hole in their soul that only God can fill?”
No. Yes, we are created with 4 parts. Body, Soul, Mind and Spirit. But, with the curse of sin from Adam, the Bible says we are born in Sin and that our Spirit is dead until it is reborn by the Holy Spirit through faith in the redemptive work of Christ on the Cross of His FREE gift of Salvation - and, it also says “But the same Spirit that raise Christ from the dead, will give Life to your mortal bodies.” - and Jesus spoke of the Holy Spirit being alive within us “rivers of living water”.
It is written in Romans 1 that God indeed has imprinted on Man’s heart God’s law, so no man has an excuse(not the native on the Plains of Africa, nor the atheist explaining away God with evolution and Nietzsche), but, it says none seek him. And as others have said - the Holy Spirit is drawing men unto Christ continually - but yes it seems like a paradox - men seeking for truth, seeking for the fulfillment of that inner void. Men not satisfied even if they gain the whole world. But - Jesus said “No man comes to the Father but that the Spirit draws him”
I will also add this - it’s a seductive thing and at the root of our sinful nature to say we DID something for our salvation. I am NOT a Calvinist Pre-Destination guy - I accept the FIRST-THINGS-FIRST construction of the verse that says “Whom He did foreknow, He did predestine”. So in the context of this thread, Men have a void, they seek for ‘something’ to fill that void. God knows that they will respond to Him knocking on their heart - and He draws them in, tells them the FREE GIFT of His redemption and then the ONLY thing they must DO ‘DO’ is their Free Will to Accept. That to me is NOT ‘works’. Not like Faith and Works as James talks about to the believer. And not like many religions to ‘justify’ themselves by works. As Christians it is also so easy to fall into the trap of “I’m good, I’m better than you, I’m righteous because of how GOOD I live my life” - WRONG. That is again WORKS.