The hypothetical idea of a self explanatory universe is nothing new. Humans have been trying really hard to explain the reasons for the existence of this universe and conscious life within this universe for thousands of years (perhaps even longer). However, despite our best minds, including philosophers and scientists, repeatedly taking on the challenge, we are not even one step closer to finding an answer. All that we have so far are a number of speculations, and even those are not without a long list of valid criticisms.
For the universe to be self explanatory, we must find a mechanism on the basis of causality which explains the existence of everything that we see in this universe including matter, energy, fields, life, consciousness, as well as the reasons for the existence of laws that govern all these things. In other words, we are looking for a way to explain a self generated and a self sustaining machine which seems to be meticulously functioning for at least billions of years in order to serve its self defined purpose.
Chances of discovering such an explanation are slim to none. However, if it is indeed discovered in the future then of course we would have falsified the claim of religion.