It's not that the Big Bang isn't the presiding theory, it's that the Big Bang theory is an observational theory rather than an explanatory theory. That is, it's a model of WHAT we see when we look into space with our telescopes, not WHY we see it. That observation hasn't changed in 60 years - everything we've seen only confirms that the Big Bang happened.

What you're talking about was noticed pretty much as soon as the Big Bang itself was discovered. Basically the observed behavior of the early universe's expansion doesn't follow the known laws of physics as we understand them. The basic analogy is that the Big Bang should have exploded like a grenade, but instead it inflated like a balloon. This obviously had major consequences for the composition of our current universe, and scientists would certainly like to understand why things played out like this. So either our understanding of physics is flawed in some way (almost certainly true, but how specifically?), or something happened during The Big Bang to constrain expansion that we have yet to identify. It could also be a combination of the two.

It's one of the great mysteries cosmology is trying to solve. No matter what happens we'll eventually get a new theory that encompasses the Big Bang plus explains why it happened. The Big Bang itself will always be a good model for what it actually describes, just like Newton's Laws of Motion are still good models for specific scenarios of Einstein's Relativity.

Exactly this.

My understanding was always that the Big Bang itself was the problem. That the specific features observed during the Big Bang don't match up with what they should be given what we know about physics. It's just a "we look in our telescopes and see this happen, we don't really know why".

So any new irregularities that JWST can find would likely be super helpful in figuring out why the Big Bang behaved the way it did, and could potentially lead to new physics as a result.

I like to say that any given Religion is a belief system, but the Scienctific Method is a disbelief system. (Literally just came up with that today, and I like it a lot.)

When scientists do science properly, they try to disprove their beliefs (i.e. hypothesis) systematically and rigorously until they simply can't find a way to disprove it. This then becomes provisionally accepted as true. However, the possibility is always there that someone will find a way to prove it false in the future, and the process continues, with each new discovery building on the foundation of knowledge that came before it.

It's the literal inverse of faith and religion.

Of course, this only applies to people doing actual science. Most people believe science the same way people believe religion - as a belief system. But IMO if you understand that the scientific method is a disbelief system, it makes believing the accepted conclusion of the Science Community much more reasonable and rational than believing the accepted conclusions of any given religion.