A few thoughts. Theists love to use an argument script like this:

1. Here is a puzzle that scientists can't currently explain
2. God explains it
3. Therefore God exists

If you accept that script you're bound to lose the argument at some point, because there will always be some odd fact that can't currently be explained. Science isn't omniscient, and never will be.

The trap is that it is very temping to try and solve such a puzzle yourself. The smarter you are, the easier it is to fall into that trap. If it's a really juicy teaser (like explaining human psychology, or aesthetics, or the origins of logical thought, or the nature of morality), then it's highly unlikely that you will succeed. A clever or experienced theist will already know the flaws (and counter-arguments) for most of the existing theories so can throw those at you. Or if you support a novel, or fringe theory (which theists haven't generally considered in the solution space, but which might work), they can dismiss it as "speculation".

What you have to defuse is the debating assumption that "God wins by default" I.e. that if there is anything at all which you can't explain, then God must have done it. When put so bluntly, it is a really outrageous fallacy that "God wins by default". Yet that seems to be what your Dad is relying on here. Don't accept it.