Fermi problems and the existence of God

In his or her article "The Math Sex Gap Revisited: a Theory of Everyone", famed scholar La Griffe du Lion writes:

"Good evening ladies. I am truly honored to be invited to the annual meeting of Women Against the Gap and even more so to be your featured speaker. I always enjoy visiting La La Land where a gap-free society defines the goal of human striving. Thank you for the invitation and for your hospitality. I confess to some initial misgivings -- after all, hundreds of WAGs in a single room can be intimidating -- but your gracious welcome quickly put an end to my fears. So, as a much-relieved featured speaker, I look forward to sharing with you a new analysis of the mathematics gender gap, which, if psychologists could do Fermi problems, would be largely unnecessary."

So what is a Fermi problem? Here is how the Wikipedia article starts.

"In Physics or engineering education, a Fermi problem, Fermi question, or Fermi estimate is an estimation problem designed to teach ... the importance of clearly identifying one's assumptions. Named after physicist Enrico Fermi, such problems typically involve making justified guesses about quantities that seem impossible to compute given limited available information.

Fermi was known for his intelligent ability to make good approximate calculations with little or no actual data, hence the name. One example is his estimate of the strength of the atomic bomb detonated at the Trinity test, based on the distance travelled by pieces of paper dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons."

An example of a Fermi problem occurred to me in the context of Christmas. What would be the consequences if God actually existed?

I know a lot of people are believers, but here I'm talking about the discovery of hard evidence that a supernatural, universe-spanning, guiding intelligence actually existed. This would surely be the ultimate intelligent alien scenario.

Don't you think that a good proportion of the Earth's R&D budget wouldn't immediately be diverted to God research? The Department of Pure and Applied Theology would surely be a branch of the Physics faculty.

I know of no country in the world, no matter how devout, where such a situation obtains.