There is a difference between the "warheads produced" and "warheads deployed," if that is what you are asking. The "force loadings" of American weapons were always lower than the total stockpile (and still are). For this reason "total warheads" is not the best measure of the relative strengths and capabilities of a country.

There isn't some kind of authoritative data on force loadings, but there are some estimates, mainly made by the Natural Resources Defense Council in the 1990s. Here are some quick graphs that just give you a sense of it. First, it's worth keeping in mind that a lot of the US weapons in the "superbloated stockpile" period were tactical nuclear weapons — "battlefield nukes" that were meant to be deployed close to front lines, or used as part of defensive measures (e.g., nuclear-tipped nukes to shoot down nuclear-armed bombers). Here is the split between those, just so you can see the magnitude of them. We don't have great estimates over deployed tactical nukes over this period; it usually just gets lumped as a big category like this.

Of the "strategic" weapons — ICBMs, SLBMs, bomber-based weapons, etc. — we have estimates as to how those were deployed based on delivery vehicle. Here's the NRDC's estimates of how those shook out. There's probably a lot of guesswork here so you can take it with a grain of salt, but it does I think correctly capture the trends and how they varied over time.

If you take the total warheads deployed in those strategic force loadings, and divide them by the number of total warheads, you get a graph like this, which shows you the deployed force as a percentage of the total stockpile. Now for reasons both obvious and subtle, this is not totally accurate — there are mismatches in the numbers in some places, clearly, hence the >100% deployment in the early 1990s. This is just an artifact of two datasets that are not totally coordinated being combined. More subtly, I am not sure whether one could count more than a handful of the weapons prior to the Eisenhower administration as "deployed," though the NDRC do. This is because this was during the custody dispute, in which the nuclear cores were not in the possession of the military but kept in Atomic Energy Commission hands. So again, take this with a grain of salt. But you can see that however rough these estimates, the percentage deployed has varied quite a bit, and during the "bloat" periods quite a lot were not deployed.

Why wouldn't one deploy them all? Because there was both a practical and strategic advantage to having "reserves." The practical advantage was that you could swap warheads in and out as you saw fit without waiting to make more, and sometimes there were times in which they found that a given variant of warhead was unreliable or unsafe and needed to be replaced very fast. (For example, one model of B28 nuclear bomb was found to not meet the standards of safety in 1962, and so was eventually replaced, which was probably a good thing since those weapons were involved in an accident in Spain in 1966.)

The strategic reason is that if you launched everything you had in one big "wargasm," then your enemy had no incentive to possibly hold anything back of their own. Whereas if you kept a reserve, you could say, "look, I could keep destroying you, so maybe we could stop this before that happens?" Now this sort of thing was probably pure fantasy, but did occasionally play a role in how the US thought about its stockpile.

Anyway, to really look at your question of "how many could have been used" in a deeper way, one has to do something like an "order of battle," which requires looking very closely at the deployed forces at any given point in history. This is difficult to do, but has at times been done. Stan Norris, whose work I respect a lot, has done this for all sides of the Cuban Missile Crisis, as a way to get a very concrete sense of what nuclear war would have looked like in October 1962. As you will appreciate one needs to get very "fine-grained" about this sort of thing.

To your question of whether the large stockpile was motivated by a desire for a "first-strike capability" (knock out all of their nukes first), that was always a US dream but by the 1960s that began to feel very unlikely. But there was always a hope that you could catch a lot of them "on the ground," and thus reduce the number that hit you, so there was definitely an attempt at a one-to-one-and-then-some matchup. The large stockpiles were also motivated by a fear (of varying levels of plausibility) that the Soviets might somehow, through incredibly ingeniousness and luck, try to catch the US nukes "on the ground" and cripple the US before it could launch an attack on them, and so having a lot of nukes was seen as a hedge against that, even in the years in which the US stockpile dwarfed the Soviet one.

The relative numbers of the warheads and missiles also should not be seen as just purely rational deployments meeting a particular end. For many of those years, they were just churning out as many warheads as they could, because that made them feel safer and because there was very little real oversight into the program. Some of those big drops one sees starting in the 1960s were in part because the White House began to take a more central role in planning and started to coordinate the nuclear war plans between the services (via the SIOP and other bureaucratic mechanisms), and the effect on the "bloat" is really apparent. So there are internal reasons for these numbers, too. You can say very similar things about the Soviet warheads too, as an aside (most of theirs in the "bloat" periods were tactical weapons).

The data from the above graphs comes from here, a now-archived website of nuclear data estimates by the aforementioned NRDC. These estimates need to be taken with an appropriate dash of salt given their inherently uncertain nature, but they are not totally made up (they are based on various declassified statements and estimates that are then analyzed by people in the open-source world). I apologize for the rough-and-tumble nature of the Excel graphs, which were hastily thrown together based on some previous graphs I have made of the data.