So one theory of the universe is that eventually the universe will collapse, "The Big Crunch". And the cycle between Big Bang and Big Crunch has cycled previously and will cycle over and over again in the future. Why weren't intelligent species able to stop the Big Crunch in the previous universes. And do you think humans in our current Universe Cycle will find a way to stop the next Big Crunch so we can continue our species in all of eternity?
Simply put, humans or any other intelligent species, and all of their toys, even if they are wildly successful at reproducing and multiplying, will always be a tiny, tiny fraction of all of the mass-energy in the universe. The vast majority of the mass-energy of the universe consists of unusable stuff such as diffuse interstellar gas, free neutrinos, stars, black holes, dark matter and dark energy from which you cannot craft tools or beings.
The speed of light, likewise implies that it is theoretically impossible for any intelligent species to have access to any part of the universe outside their light-cone, which is the vast majority of the universe.
To change that outcome, one would have to somehow profoundly change the distribution of mass-energy of a significant share of the other stuff in the universe (the vast majority of which is known to have essentially no non-gravitational interactions with anything else), which would be many orders of magnitude greater than the mass-energy of everything that they are or control, and would need to impact a much larger share of the entire universe than they will ever, even theoretically, be able to come into contact with.
What you propose would be more difficult than it would be for a colony of shrimp originating in a single ocean floor thermal vent, to empty the Indian Ocean and turn it into dry land.
This really is impossible because the disparity of scale between any intelligent species and its maximal range of spatial distribution, and the total scale of the universe is just far too vast.
A technical explanation of the physics of a Big Rip or Big Crunch can be found in this power point presentation by a physicist.
TLDR: To stop expansion you have to reduce the gravitational attraction of the universe by removing mass or increase the 'push' from expansion
A bit of background
Essentially we don't know exactly what will happen. The fate of the universe is, we think, governed by the density of matter in the universe (vacuum energy also comes into it) this fate is described by the Friedmann equations.
The "Big Crunch" is used to describe the case where the mass density of the universe is high enough for the gravitational attraction to pull against the expansion of the universe, stop and eventually reverse that into a collapse.
To calculate this critical mass density we first need to know the magnitude of other components it is to balance with, including those for Dark matter and Dark energy.
You may or may not be aware but there is still a lot of research to be done before we can figure out what these components actually are and it is difficult to do so from one point in time as illustrated in the image below.
The orange curve represents a closed, high density universe which expands for several billion years, then ultimately turns around and collapses under its own weight.
This is your "Big Crunch", for completeness I've left in the description of the other three curves below. However, as you can see the lines all look very similar from just one point in time. We only know what the universe looks like 'now' so cannot definitively say which of the four is our universe's fate.
The green curve represents a flat, critical density universe in which the expansion rate continually slows down (the curves becomes ever more horizontal).
The blue curve shows an open, low density universe whose expansion is also slowing down, but not as much as the previous two because the pull of gravity is not as strong.
The top (red) curve shows a universe in which a large fraction of the matter is in a form dubbed "dark energy" which is causing the expansion of the universe to speed up (accelerate). There is growing evidence that our universe is following the red curve.
Assuming we are in a closed universe
So, for the sake of your story, we can imagine that in the future we use data gathered between then and now to know which fate our universe has in store (by comparing the data points between ~now and your future time)*.
Your scientists would need to figure out a way to counter the gravitational collapse before the universe reaches the peak of the orange curve (view that as your point of no return).
The ways this can be done is:
Destroy matter....and a lot of it. Possibly through matter-anti matter interactions. First point is that you cannot create anti-matter without also creating matter, however it is a big conundrum as to how our universe has so much matter and we don't see so much anti-matter. Perhaps your future humans discover some far off galaxy cluster made solely from anti-matter and crash this into another one.
Find a way to drive the expansion of space - This lies entirely in science fiction as we aren't sure what originally drove, theories point towards positive vacuum pressure or a negative vacuum energy density but no one knows for sure. This is your story...you can have your scientists be doing these things without having to explain why if you like. You're already writing about a time several thousand, if not hundreds of thousands, of years in the future so you have a lot of freedom for what technological advancements we have made.
*Your future time would have to be very far in the future, given the scale of the graph we wouldn't be able to determine which of the universes we inhabit without a few thousand years at the very minimum.
I'm not sure whether the Big Crunch is accepted nowadays as the future of the universe. But, as far as I know, it depends on the energy density of the universe. If it's too low, it will expand endlessly, if too high, it will collapse. So we can not change its fate.
Just as humans have currently reached the point of being able to affect the Earth (in particular, climate change), a K-Ⅲ civilization will mess up the natural order of whole galaxies.
Suppose that they have some kind of hyperspace FTL technology. This allows such meddling to violate the normal concervation laws and lose mass-energy to “outside”. The K-Ⅳ equivalent of our CO₂ emissions may be hyperspace pollution as it is used as a sync for their “unlimited energy” devices. Mass vanishes from the universe,on a scale that affects the topology of the portion of the universe they’ve reached.