[Atrocities]

I remember having this very same discussion over two years ago on a long since dead Star Trek fan site. How did the Federation arm so quickly after the loss at Wolf 359 to the 600 plus ships of each fleet in the Dominion War?

The official Star Trek answer is refurbished mothballed ships, rapid development and construction of new ships, and purchasing of ships built by other parties to Federation standards.

Until the Borg attack the Federation was a research and exploration focused society with few ships for fighting. They had in fact had an on going conflict with the Cardassians as described in the 4th season episode called "The Wounded" where we were introduced to both the Cardassians and the Nebula class star ship.

Following the Borg attack the Federation began a crash course in ship design and construction, and from that the Akira, Sovereign, steamrunner, intrepid, and defiant class ships were born.

Think of it as well, like the beginnings of a SEIV game. At first you’re dedicated to exploration, until you meet a hostile enemy, then you begin researching new weapons, and ship designs. You then begin a rapid production of these ships in anticipation of war.

That is essentially what happened in the Trek universe.