So no matter where we look, some light from some galaxy would have reached us already.

Well, two things.

No matter where we look, light *is* reaching us. What we used to think of as dark patches of sky turn out not to be, they’re just so far away and so faint that we can’t see them with the naked eye, or the first generation of telescopes, or the second, but now comes another quantum leap in telegraphy and suddenly, whoop, there it is.

Second, my “theory” is that the universe is not infinite, but is being “created” at the margins. That is, there is “nothing” - true nothing, not just vacuum but the absence of anything, yet somehow at the margin “somethingness” is being created (time & space) after which the physical manifestations that we can understand (quarks, atoms, protons, eventually hydrogen, matter, etc.) moves in - which is why space continues to “expand”. It’s not that new stuff is being created, just the framework of space (& time). So everything continues to move away from everything else, perhaps forever.