Some people have proposed this at least ever since the first suggestion that the Bohr hydrogen atom was a typical atom with electrons in circular orbits around it.  Possibly the idea is even older, though I cannot think of earlier suggestions than that.  Quite a lot of earlyish SF used that theme, but it has worn thin since about the mid 20th century.

Nowadays there might still be some New Agers or similar nuts with such ideas, but I can't remember hearing about anyone serious about it.

Personally I regard the idea as nuts, but not substantial enough to make detailed discussion worth while. But feel free to correct me.

The idea is very old - this is what Wikipedia says:

Macrocosm and microcosm is an ancient Greek Neo-Platonic schema of seeing the same patterns reproduced in all levels of the cosmos, from the largest scale (macrocosm or universe-level) all the way down to the smallest scale (microcosm or sub-sub-atomic or even metaphysical-level). In the system the mid-point is Man, who summarizes the cosmos.

Part of it is so far turning out ot be wrong - the structures are not the same, they are so different that even the laws of nature become a bit different.

Part of it is so far turning out to be true - what seemed to be the smallest turns out to HAVE a structure again, what seemed to be the biggest is part of something bigger (OK, not quite, as we see even another galaxy with our naked eye and always knew the object was there, but it took time to find out that it IS a galaxy).

I personally think our universe IS part of something bigger (though I cannot argue or prove that) but not something you can describe by analogy from other scales.