We can observe what is beyond the edge of our galaxy. Our telescopes - like the Hubble and Webb - are powerful enough to capture the light of distant galaxies and from that we can see that they are made up of stars just like our own. The Ultra Deep Field is one of the most awe inspring photographs ever taken - each dot of light another galaxy out there like ours.

Too far beyond that, though, and we don't know. There is an edge of the observable universe beyond which we know nothing - the universe literally isn't old enough for light to have reached us from anything beyond this horizon.

We guess that there is nothing special about this boundary and that whatever lies beyond it is the same as what we can observe, but its just a reasonable guess as we can't have any direct observation.

We can see other galaxies pretty easily with a telescope, what we can’t see is way farther.

It's not a guess, we can see it! For example, here's an image from the Hubble telescope of one galaxy pulling material from a smaller nearby galaxy. So now we know that's a thing that happens - and we're not just guessing, it's something we're actually observing happening.

BTW those two galaxies are 200 million light-years away. For reference, our own galaxy is about 100K light years across. So that's an event we're directly seeing that's about 2000 galaxy-widths away from our own galaxy.

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Because we can just see it. You can see other galaxies with the naked eye, and with expensive telescopes we can basically see infinite. So no it's not a guess

We just look. That's what telescopes are for. It's not anymore complicated than that. There's nothing special about inside vs outside our galaxy. It's not some barrier. We have extremely powerful telescopes that can see to the edge of the observable universe.

The only hurdle is in accurately measuring distances to other galaxies. But we can do that with a bit of math and physics (of supernovas specifically. They're called "standard candles").

Other than that, it's just looking. The sky is literally there.

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It's all our best guess; however our best guesses matches up very well with most of our predictions. This implies that our guess was pretty good.

For example, we predict that the sun and pretty much all others main sequence stars have an abundance of hydrogen fusing into helium. We've never grabbed a bit of the Sun to analyze directly (let alone any other star), but we still believe them to be made primarily of hydrogen. Our physics and cosmological theories make predictions like the spectral nulls, orbital rotations, etc.

That said their are several discrepancies, like differences in the calculated value of Hubble's constant depending on how it is generated. These failures of our predictions are actually some of the most exciting results for scientists since it indicates that there is likely some new physics there that we don't fully understand.