I'm talking about "Broken Bow." What you're talking about is two years later.
But there was no Klingon threat in "Broken Bow", just a small craft crashing. For all we know because UESF shot it down! Certainly the
Intrepid would have existed at that point if starship construction takes as long as the later events would indicate it does.
What evidence is there that any and all ships SF had weren't being used for exploration (and related support) within their limited range
Chiefly the lack of exploration procedures evident in our heroes' stumbling. What would Starfleet have explored when there was nothing actually found by them? We learn of no encounters with alien species between the Vulcan arrival and Klaang's - except those made by Earth's civilian truckers.
As has been pointed out, the U.S. Navy "existed" for a nearly half a decade before any ships were built, let alone on the open water.
But the existence of ships is hardly in doubt - ships exist in "The Expanse" and decidedly lack novelty value there. They even represent "generations", some looking like Archer's scale model and the spacecraft in the opening credits, another looking pretty much like the
Enterprise.
Most of the "traditional", 24th century (or 18th century) naval roles would be difficult to perform with ships that can't reach their destinations until months or years after the call for action. Combat is the one thing that could be performed, because in the typical case the enemy would do the traveling for you! It is also the role in which Earth would no doubt place its greatest ambitions.
We have the organization. We have the personnel. We have the limitations on what these might be doing. We don't have an explicit limitation on the combat role being performed or at least practiced for or on the required ships existing. The "early US" naval model certainly could work here, but it's not one we
should greatly favor over the "UESF was made battle-ready just in time to kick Kzinti tail".
But in an unprecedented situation, meaning there might not be any precedent to what she wanted, either.
And again, there was no war so wherefore a "warfleet"?
There's always war in Trek, especially when none is mentioned! And conversely, there's no mention of peace between the Vulcan first contact and Klaang's arrival.
But by historical precedent, navies are formed when a nascent nation can afford to, in order to have war - what gets founded in
response to war is a more haphazard arrangement that generally fails to persist. The US deliberately sought for combat after acquiring the means, but reasonably not before spending some time training for properly using the means. The situation in the new South American navies of the 19th century might be even more appropriate, with modern fighting vessels acquired more to introduce an all-new dimension to fighting than to meet an existing need.
At its conclusion NX-01 receives new orders to continue with its initially planned exploratory mission since they are already some distance from Earth.
Those were Archer's own orders sent back to him with official blessing and lots of snickering behind the Vulcans' stiff backs. Forrest just "saw no reason" to stop Archer from doing what he was doing anyway, now that Archer's actions had created a done deal.
It's only because of Archer's hissy fit making them lose their cool that they temporarily withdraw and later come to a compromise to allow SF to carry out the mission—with T'Pol's direct oversight.
And Archer continues to hiss, for one thing sailing outside Vulcan reach and threatening to sail further. So it's the Vulcan "authority" that has become irrelevant here, through this introducing of an all-new element to the UESF.
With the fleet that we've seen in ENT, and allowing some extrapolation, we have less than a dozen warp-capable ships in Starfleet (or equivalent agency).
Or then about a hundred, 90% of them stuck in transit due to their inferior engines.
And that's just "capital" ships (or what goes for a capital ship in Starfleet; heavy cruisers seem to qualify a century later). We have seen that the tiniest arctic survey sleds are warp-capable in the 2150s, and those might have some sort of a combat role even though they have no real interstellar role. A massive military organization might exist for juggling such "coastal" assets, just like South American navies were founded around highly capable monitors that nevertheless were quite incapable of ocean transit.
Timo Saloniemi