You understand the situation succinctly. We are not alone. Only problem is the huge size of universe. Light has not yet arrived on earth from far away galaxies, that is how big the universe is. Our own milky way galaxy is so huge, our spacecrafts are unable to escape it. Each of the zillion galaxies have zillions of stars and each star has planets. Life forms if the planet is exact correct distance from its Sun to achieve moderate temps we have on earth. Other planets in our solar system are either too hot or too cold. But since the number of planets in the universe is unimaginably large number, probability is very high that life exists on zillions of planets. Too bad the distances are so great. To make things worse, the universe is still expanding!
You have correctly repeated the official wisdom of “science” cosmology.
The problem is that most of it is garbage.
You can’t verify any of it with actual observation or personal experience—you are just repeating what the “experts” say.
Good luck with that.