>It's clear that in our modern era, with our extremely robust theories of physics, backed by extremely precise observations of the universe, that the religious explanations of existence are false.
I think that's up for debate still.
I think that's up for debate still.
Some conspicuous examples have certainly been falsified, like young earth creationism, but that certainly doesn’t mean that all of Christianity’s claims have been falsified.
The classic counter-argument is that God has created the world N years ago in a way that makes it appear older, in order to test our faith or sth like that.
You cannot really disprove that. Scientists discard such theories because of Alder's Razor: "What cannot be settled by experiment is not worth debating."
I think your misconception is that science is the method by which all truths can be discovered. That has not been shown. Science is merely a narrowed down version of philosophy (with restrictions on which tools and methods may be used) that is vastly better at finding a consistent and useful model of reality than average philosophy.
This is why something like Occam's Razor (or Alder's Razor from above) is used by scientists. Occam does not say that the simpler hypothesis is always correct, but it suggests that you will usually be more productive when you work with simpler rather than more complex hypotheses.
Here’s one article from them: https://answersingenesis.org/age-of-the-earth/
"Now that we have developed tools and processes for validating truths against falsehoods which seem to be accurate across all applications thus far - for a religion to exist it must violate one or more of the rules that are true elsewhere or bypass these rules entirely."
So "false" vs "unprovable".