But we don’t have any basis to say it’s impossible.
We have no basis to say it's possible, either - as I've stated before, this entire sci-fi trope is based on nothing more than techno-fetishists trying to conflate consciousness with information technology... and sci-fi tropes doesn't get more wonky than that.
It could be a thousand years or a million years.
Considering that we'll be lucky if we can maintain Victorian-era levels of industry by the end of this century, I'd say a fallacious belief in "progress" is rather inappropriate these days.