Not really. The great filter idea is only one of many proposed solutions to the Fermi paradox. The Dark Forest hypothesis would have the universe filled with life, which is all in deep hiding from an intergalactic civilization hellbent on destroying all other life.

Personally I think the great filter is a dumb idea for precisely the reason you posit. The universe is (probably) infinite, which means there's an infinite probability that we aren't special or alone. Maybe we're the first; the universe is (relatively) pretty young from what we can tell. I doubt that too, but I think it's one of the most plausible explanations.

But really what it comes down to is that in an infinite universe, the probability of anything happening exaxtlt once is infinitely small. It is infinitely more probable that there is or will be other life out there.

Really, out of uncountable trillions of planets in trillions of galaxies across tens of billions of years, how could it be that exactly one planet can produce life? I think it's egotistical navel-gazing in the extreme to assume we're alone.

If you take the beginning of the cosmos to be 1 second ago, the point where other galaxies will be unobservable is in just a few seconds (at T+7–8). We’ve only had civilization for about 700-800 nanoseconds. You could fit hundreds or even thousands of advanced civilizations in there and they’d never know the other existed.