Perhaps I'm not understanding the question, but first and foremost, science is specifically not a belief system. My professors emphasized the fact that we were not to believe anything but rather accept or reject hypotheses based on evidence. Science is a tool. It's a system of observing, recording, hypothesizing, testing, analyzing, and refining. If you're asking when we will have refined everything to the point that there are no more questions, I don't think that will ever happen. What I've found is the more questions you answer, the more questions you have.

I remember reading an article (can't find it right now) from a PHD dropout who was doing research in string theory. One of reasons he dropped out is his frustration at how abstract and disconnected from reality his work was. His advisor (and his colleagues) didn't have that problem, because to him, the math behind string theory was an ends in itself. There's beauty in math, regardless of whether it has any practical application. If string theory turns out to be an accurate model of reality, then that would be a nice bonus, but that's not why his advisor studied it.

So to answer your question, if we somehow reach the point where everything that can be feasibly discovered has been discovered, then theoretical scientists would make up their own models and study those.

When Science ceases to be useful as a method to discover and explain things.

But on a more specific note, that's impossible to answer, because you would have to know what that finite set of "knowledge of everything" is, if it is indeed finite. Since we can't know what the upper limit of "what is knowable" is, it's impossible to even roughly project when we might know almost everything.

To complicate matters, you can't even break the problem down. How about half of everything? A third of everything? One-tenth of everything? How much do we currently know compared to those subsets? We simply don't know.

And what if we discover other dimensions? Or what about another universe? What if there's infinite universes to discover? Knowledge is emergent as a result of doing science, so as long as there's something we don't know, we'll have scientists out there doing science (or whatever its successor is).

Just an amateur opinion: If we think of science as a beliefsystem (a system to arrive at a close approximation of truth), it is much more adaptive than any other explanatory system. I think for that reason alone it will 'win' in the long run, but emotional systems will carry on/blossom in some form or another as societal breakdowns occurs, or if Science incentives gets compromised by ideology/money, thereby resulting in less trust.

If we look at what science already know, some Physicists, (carrol etc) believe we already have an 'engineering corpus' of everything we see on a daily basis, but as soon as we look at the edges of non-human scales/focus there's a lot to find yet.

Even if we ever find a theory of everything and know all the primary forces, we still need to learn all the ways these forces can be combined, and we cant readily predict 'interesting phenomenons' down the line from an algorithm, so exploring will continue in our current reductionist exploration, but will perhaps pivot to a more holistic exploration. Steven Wolframs 'ruliad' is supposed to contain all possible combinations of everything and all their derivations (forgot the def. ;) ), and he talks about theoretical science realms that we will have a hard time even seeing/understanding. Some argue that the primary forces also varies across the universe. Chaos theory argue that it will take endless energy to collect endless dynamic data - even if we compress it into math/axioms etc. All exploration of chaotic space will take time to compute. Also, If we want to utilize our knowledge we need to either store/retrieve, or compute based on data/algorithms. In Billions of years this use/pursuit of knowledge will cost a lot of energy.

There's a lot to think about in such a question, but it's interesting how we can send shit to other planets, but we completely lack the knowledge/technology to manage a large ecosystem, or organize our self in a way where we don't harm each other or our habitat. The first is very easy compared dynamic systems. I don't think we've even scratched the surface of what our dynamic systems can do for us if we learn to tame them.

Anyway, in the long now, thousands of years, I think the system of Science will evolve, improve, but we will not reach 42. There will always (billions of years) be combinations of forces that we cant predict easily and some we have to explore/create to discover/enjoy.

It got a bit messy, sorry..

Oh well, you should ask how long does dark age last instead. And it is far from over, many countries in the world embrace ignorance and conformity.

Once we determine if the universe is infinite or not we’ll know more about what to expect.

If it’s finite then we’ll have a stopping point. If it’s not then there’ll be no stopping point.

Assuming a finite universe then I’d wager we’ll know all that can be known in about 10^23 years.