Loss and lots of science and math to model and simulate the sun in a variety of ways slowly weeding out the models that weren't making experimentally validated predictions. I'm not sure how many astronomers are around, especially sun focused ones, on Lemmy to answer you more specifically about the history of sun science.

The sun is based on physics and observing nebula and super novas. We know how much the sun weighs based on it's gravitational pull. We know what it's currently burning given the frequency of the light it emits. We know what generation it is based on the elements in the planets. And we know the contents of other stars by the light they emit when they explode and collapse.

We know the layers of the earth because we can bounce sounds off the earth's core to see how deep it is. We know roughly what it's made of because we know how much the earth weighs and that the earth has a magnetosphere (you only get that with certain metals).

The methods used are generations of built up knowledge in physics and astrophysics.

You can, of course, just google these questions and get better answers than my summation

https://manoa.hawaii.edu/exploringourfluidearth/physical/ocean-floor/layers-earth#:~:text=There%20is%20evidence%20that%20the,generated%20by%20earthquakes%20or%20explosions.

You're only off by about 9 zeros.

5 trillion K is a lot more than 5500 C.

adiabatic detonation temperatures also top out at some 4500C even for the most energetic explosives

What if we pre-heat the room to 3000, then very quickly introduce the explosives and run away before detonation?

Surely a laser would be way more practical

I only vaguely recall this, but I seem to remember reading that using lasers we can actually get things into the negative kelvins? Or maybe we get them so cold they become hot? TBH I can't remember and it confused me when I read it, but I remember it being a reputable source

Edit: yeah this is evidently a thing