War footing doesn't mean that you are currently or recently engaged in battle but rather that you have a large standing military or dedicate a large portion of your GNP (or interstellar equivalent) to the military in the event of future conflict.
But when it's established the Dominion does not wage wars, it follows it's very unlikely to have a large standing army.
Indeed, the very fact that its soldiers are invisible only when not fighting
is splendid support for them existing for reasons other than fighting of wars. If your troopers are invisible, nobody can tell they are not
there or that there are less of them than the rumors say.
Note that despite all the bluster, the Dominion never manages to send troops to blockade the Gamma side of the wormhole. Instead, they bide their time, then send troops to blockade the Alpha
side in a complex plan requiring local allies. If they can't hold an initial advantage even on their own turf, they are unlikely to be in any sort of "readiness".
But if we were being serious, if the Dominion had existed for thousands of years before the Federation (aka space flight and other advanced technology) then how did they not have such a technological advantage to crush the Alpha Quadrant races like roaches?
The dialogue references are to about ten thousand years of existence and two thousand years without credible opponents. That would be an obvious recipe for stagnation - especially as the Founders have every motivation not
to teach their subject races how to become superior soldiers or build superior weapons! A police state doesn't arm its police with tanks, lest their barrels be turned against the presidential palace; batons, tear grenades, water cannon and submachine guns are plenty enough to deal with the average mass of disgruntled citizens.
So I guess after the Dominion reached a certain point of advancement they just decided to hold firm
The thing about the Dominion is that it does not decide. It is not the government, it is the subject and the victim. The Founders lead, and it is in their interests to keep the Dominion weak.
It's a devious setup, with a dramatically satisfying Achilles heel. And it's not without historical precedent, as the Nazis made damn sure their military forces were in a subjugated position, deliberately starved of resources and at the mercy of an obscure and inefficient chain of command. It worked very well for a while, and then backfired big time against an actually formidable enemy with enough resources to take losses and make mistakes and still triumph...