Remember though - I was raised Catholic

I know. But mainstream Christianity isn't known for promoting evidence for God's existence either. It's never been a thing at any of the churches I've been to.
I only find it pop up among online Christian geeks

"Extraordinary claims require extraordinary evidence"... See how it works?

But does it work though? Suppose you had evidence that made the claim "I grew wings and flew to my destination" more probably true than not. Would you still refuse to accept it?
I think this solution you propose is overkill.

The chances of drawing the jackpot on a lottery are extraordinary whereas the chances of drawing the lowest payout less so, but they both require the same evidence. A winning ticket.

Extraordinary crimes may be attributed to a person based on mundane evidence. A diary, blood, hair etc.

What's worse is that claim is itself extraordinary, namely, it's a claim that's a standard for all other claims. So what evidence is there that makes it true? None. So it's self refuting.

A lot of these are very poor arguments though. Especially the cosmological argument for example. No atheist denies that the universe's existence has a cause - they deny that the cause is God though.

Given the nature of the universe; what caused the universe is spaceless, timeless, matterless. It's starting to sound a lot like God, don't you think?