To add to my previous post, here's a more specifically quantitative discussion:
From planets to the Oort cloud, the total amount of non-gaseous suitable material for processing by self-replicating factories in a star system like the solar system is
roughly on the order of 1E24 metric tons, a
trillion trillion tons. (The total mass of the solar system is about 2E27 metric tons, three orders of magnitude more, dominated by the mass of the sun
itself, but the preceding is looking at accessible material which is neither in the sun nor gaseous).
Consider a civilization approaching the limit of such natural resources and having 1% or more of the preceding in the form of warships and other military hardware, under the assumptions described in my previous post.
Then the hard sci-fi civilization has on the order of 1E22 tons of military bases, warships, etc. per star system. For perspective, considering the limits of Federation industrial
capability, the Federation does not appear to have more than around 1E9 to 1E10 tons of ships at most. This is literally a difference factor of around a
trillion times between the amount of Federation military hardware and the amount in each star system of such a hard sci-fi civilization.
Technically, the opening post scenario doesn't limit the hard sci-fi civilization to a single star system, so one could even consider a hard sci-fi civilization which was over a non-trivial percentage of the 0.4 trillion star systems in the galaxy, in which case the Federation could have to waste time trying to destroy
billions of trillions of times Starfleet's mass in military hardware in a reasonable period of time. (Different star systems previously colonized by STL expansion can not directly help each other during the timeframe of a war, as long as they have no FTL, but they mean more targets for the Federation to have to destroy before any one obtains FTL from a non-Federation ship visiting).
In my previous post, I mentioned how there will tend not to be a quick Federation victory when the Federation does not have trillions of megatons of firepower, but this shows it in more detail.
Federation ships can be literally outnumbered a trillion to one even if their whole fleet is sent into a single star system at a time, and the limits of their capabilities mean that Federation offense will tend to be a slow victory, if such does occur.
Ironically, in some ways, this actually reminds me of Harry Potter (wizards) versus the modern world scenarios.
Of course, it is not a perfect analogy, but let's look at how an analogy can be made:
One side of the conflict is a small group with greater abilities, ideally able to attack at will anywhere while their homes are inaccessible from any counterattack, but they have such orders of magnitude fewer numbers that they lack the demonstrated ability to do enough fast enough to fully win the war in anything short of a long period of time.
In the Harry Potter versus scenario, the situation can be a small number (like dozens) of Death Eaters with the demonstrated ability to kill not many times more than their number per day, instantly teleporting anywhere through apparation. That's questionably effective when the world has a population of 6 billion with a natural death rate and replacement rate upwards of a hundred thousand people a day. People can imagine the Death Eaters using innovative and vastly different techniques to nevertheless quickly win the war (e.g. true brilliance controlling and manipulating governments against each other), but such predictions are uncertain. They canonically have not shown such effectiveness in the past (failing at the task of finding and eliminating one child), rather frequently demonstrating tactical incompetence.
If some other wizards make a deal with the orders-of-magnitude more populous and massive muggle civilization, in exchange for a variety of possible motives and material benefits, the small group's capabilities can become no longer unique. At that time, the small group may end up in trouble.
In this versus scenario, the situation can be a proportionally small number of FTL warships with only the demonstrated number of megatons firepower each to destroy not many orders of magnitude more than their own number per mission. That's questionably effective when the hard sci-fi civilization can have billions of trillions of tons of military hardware per star system, slowing the progress of the Federation assault force due to outnumbering them literally by a factor of around a trillion. People can imagine the Federation using innovative and vastly different techniques to nevertheless quickly win the war (e.g. supernova warp missile barrages), but such predictions are uncertain. The Federation does not appear to have canonically used those tactics in the past (losing to the Klingons in the alternate timeframe, etc), and it frequently demonstrates military incompetence.
If ever some other warp-capable groups make a deal with the many-orders-of-magnitude more massive HSF civilization, in exchange for a variety of possible motives and astronomical material benefits, the Federation's access to FTL could become no longer unique. At that time, the HSF civilization might indirectly have a chance.
In mass terms, there's a greater potential difference between an advanced HSF civilization compared to modern earth's civilization than between modern earth civilization and a stone-age tribe. In raw mass terms, a civilization thousands, millions, or billions of years beyond today's civilization could theoretically be more beyond us than modern civilization is beyond the largest tribe of 10000 years ago. Given sufficient time, self-replicating technology can allow a HSF civilization to utilize on the order of a septillion tons of suitable material per star system.
Yet the Federation is a civilization that instead is one of the main powers in a galaxy of ~ 400,000,000,000 stars while nevertheless having a total of 150 member worlds. The Federation instead has a mass of structures and equipment produced closer to modern earth's civilization in raw tonnage terms (albeit far more technologically advanced than modern earth, of course). The Federation is more at the billion-ton level than at the trillion trillion ton level. The Federation has the industrial capability to build on the order of 100 ships per year or less, not billions of ships, not trillions.
Despite the preceding analogy, if the Federation is smart and ruthless, they could win this scenario. Such a Federation manufactures and deploys supernova warp missiles.
Meanwhile, they promptly blockade space around the HSF civilization to prevent any non-Federation starships from investigating the intriguing massive new civilization that has appeared in the galaxy. Assume the Federation is fully successful in such. That's both to prevent any starships from risk of being captured and to prevent any from making a deal under superintelligent persuasion. After all, the Federation doesn't want a situation where any powers unfriendly to the Federation act like the U.S. did when the Soviets invaded Afghanistan by supplying nonindigenous technology to weaken a common enemy, nor Ferengi looking for profit, nor other complications.
Assuming the HSF civilization's emergency assets aren't spread over an excessive volume of interstellar space for full destruction and assuming the Federation manages complete genocide without excessive hesitation, the Federation wins. If all goes to plan, the HSF civilization never has a chance, never getting any access to FTL before full destruction, being a sitting duck.
But I'm not convinced that's how the Federation deals with hostile interstellar powers, and, as a result, I suspect that a HSF civilization so many orders of magnitude more massive than the Federation may have a chance.