Yup! Current mathematics says very hot state at very small, dense volume in the very distant past. I wouldn't include "observations" in this statement as what you're discussing is based on using known observations and going backwards. It's more of a "indirect observation."

A few things you're misinterpreting are about the Point itself which I'll capitalize for clarity and define as "the atom-sized moment in time and span where the universe was very hot & very small." Mathematically, there is no before. There can't be "negative time". Yes there is the past, but the Point is t = 0. There is no time before 0 in reality (though there is in math obviously)

The Big Bang doesn't happen before the Point. It is the explosion that occurs when the Point cannot contain itself any longer. Again, there is no negative time in reality.

Yes! The data is extrapolated from known observations i.e. we know the stars in the sky are getting farther away from us, so if we do the math and go backwards, then the universe must have started at a single point. And again, if it is a single point, that all the matter in the universe makes it very hot and very dense.

Yup! When anyone says there was "nothing before" they're typically using the math in their favor. Remember that math is just math. Numbers being numbers. Some human as to interpret them. So, if universe is expanding, then in distant past it was a single point. If universe was a single point, then even before then, it was nothing. These folks are using the "negative time" that makes sense on paper (in math), but doesn't make sense in reality. Again, remember "negative time" is not the same as "the past." You can go back in time in math or theoretical reality but you can't have time before time even existed.

There is every piece of evidence that anything/everything was 'created.' You're misinterpreting the when of the Big Bang. Big Bang happens sometime after t = 0. That explosion is used to explain when the weak/strong intermolecular forces began to actually work. There was space now for sub-subatomic particles to exist. So nuclei formed. Then gravity began to exist. Then literally everything else happened.

I agree that the Big Bang is romanticized but if you're reading up about the Big Bang in outlets that write about it that way, you're not looking in the right spot anyway.

It's romanticized in high school or young children's programs because this topic is several decades of lectures/papers/experiments. How do you expect to get people to do science or math, if they think it's inherently boring?

Again, it's rooting in math. It's not guesswork, we're working backwards. You even mention this yourself.

It's not that we know less than we think. It's that everytime we answer a question, we come with 100s of other questions. We have to make sure we're right. We don't just stop?

Calling the Point the "Hot Dense Universe State Snapshot" would be correct. The Big Bang is the part that happens after.