Earth and the military forces tasked with protecting its citizens had
already "lost millions to the Xindi" from the moment of the attack on Florida, which would doubtless be viewed as an act of war, so it's not actually
necessary to postulate more than that to explain this particular reference of Edison's (although it's obviously
possible to do so, and some may find it desirable). Besides, whatever losses to the Xindi he was describing were lumped together with those incurred during the Romulan War(s).
Besides Archer for four years telling and then showing that he's doing all of this stuff for the very first time, despite being Starfleet's hand-picked explorer, there's Cochrane's speech about the Warp Five Engine being necessary for any sorties into the truly unknown (and nobody had it before Archer), Forrest being convinced Archer will make history every light year...
Because of her unparalleled speed, NX-01 was making history by pushing the frontier much
farther from Earth than had been possible up to that point,
expanding the reach of exploratory efforts to include "thousands of inhabited worlds" as per Cochrane's words. But there would have been plenty to explore
within their limited former range in the decades prior to that, even if Forrest would consider this still merely "wading ankle-deep in the ocean of space" by comparison to the far deeper plunge NX-01 was poised to take. In an ocean as vast as space, there must be a great deal to discover and map and catalogue and study even just up to the point where you've barely gotten your feet wet. (Heck, perhaps just within our Solar system! We know from "Strange New Worlds" that Archer and Tucker once went on a "training mission" to Titan. What better way to train explorers than by having them explore their own backyard?) And even if there ultimately
did turn out to be relatively little of interest worth mentioning, that doesn't mean they didn't go looking.
It's not as if there would be a shred of evidence for Starfleet having explored anything before Archer.
What of the
Neptune-class survey ships in service for "over a decade" before NX-01 as per "Singularity"? I would certainly consider surveying to be a form of exploration. (Incidentally, as I looked up that reference just now, I initially thought it might raise a potential inconsistency with the "First Flight" timeline discussed above, in that they are described as "Warp 2 ships" and the episode is dated to August 2152. But this is entirely obviated when considering that such a rating is a theoretical upper limit, and "breaking the barrier" means
exceeding it, as Robinson did the instant he hit 2.1 in the NX-Alpha. This tallies with NX-01 being classed as a "Warp 5 ship"
on paper, but not actually achieving that speed until "Fallen Hero," and even then being caused great distress and unable to sustain it. Thus, Robinson and Duvall were not the first humans to
reach Warp 2 and 3 respectively, but the first to
surpass these benchmarks. Completely obvious really, but just thought I'd clarify since I was thinking it out.)
Also, Starfleet's motto was seen to be
Semper Exploro ("always exploring"), though I suppose it's true we didn't actually
see this phrase in evidence until the third or fourth season of ENT.