Naah - as others have said you have got your series in a twist. DS9 was deliberately vague about fleet sizes just like the other shows, however. Starfleet probably lost about 200 starships during Operation Return, easily built in a year in any case or they would have lost the war.
The most solid figure on overall fleet size is the estimate that the available 1500 Klingon ships in the last few eps of DS9 are outnumbered 20 to 1 by the Dominion fleet, Cardassian, Breen, Jem H'Adar.
Presumably to engage them, the combined Federation, Klingon and Romulan fleets must be that same approximate size. The Federation seem to be the leading partner, and the Klingons can only spare about 1500 ships (maybe 25-30% of their entire fleet) so you have to assume Starfleet has approximately 15,000 ships to deploy.
That is, however, all ships, everywhere. The Federation seems to be vast and large chunks of it not involved in the war would need to be defended. Also there would be garrison ships, convoy escorts and ships not at all suited for combat from choice. They would also, at least at the start of the war, be all over the place, some years away.
This is how you get the situation of Starfleet in TNG using fleets of dozens whereas suddenly they have hundreds in DS9.
In peacetime, Starfleet needs far fewer ships, so presumably very many spend a lot of time in mothballs, hence the sudden huge number of disposal Mirandas, Excelsiors and kitbashes during the Dominion War.