It is interesting how each of you asks different questions. You ask
"Can Science......" while Agobot asks "Does God.....".
Since this question is in Faith/Belief, I suggest that we presuppose that God
does or
could exist and then go from there.
God is not, IMHO, merely a product of our minds, although some who I argue with claim that each of us create our own ideas about Him. (I would argue that God created us long before we even had the ability to create/imagine Him but, of course, I cannot prove it.)
Logically, the way that I will approach this question is to ask if God ever
needed to have or to at least experience emotions and, if so, what for?
This leads us down the path of asking whether God is too awesome and beyond comprehension to ever be understood or whether God made it possible for us to commune with Him and understand Him based on His becoming like us for that purpose.
If the former, we are likely gods ourselves in that we prefer scientific inquiry to increase our understanding and don't even necessarily need a relationship with said Deity.
If the latter, we are probably talking about the mystery and legend of Jesus Christ.