Psalm 23 is a wonderful and calming prayer that I've known for years and I still say it on occasion to help me get through daily life. And if you believe Jesus is God made flesh (even though Jesus denied that) then good, that belief brought you to a relationship with God. Churches teach that Jesus is our Lord (God) and Savior and if people believe that it is Jesus that sent them that warm and peaceful presence then that is what "Jesus" did. Still, it wasn't "Jesus", it was God. I doubt God cares how you find Him, as long as you do. If you ask Jesus to take over your life you're really asking God to do that so the words are interchangeable. Either way, the person gains that experience because they equated Jesus with God. Jesus did say that he came to show the Way but denied "being" the goal of the Way, God.

As you said God offers the same relationship to all. But many are called and few listen. Only honest seekers of truth will pass through that narrow door.