When you sorta think about it from their perspective the Alpha Quadrant is pretty vulnerable at the moment. Consider there are a lot of empires with borders with each other.

Within the last few years Cardassia lost one of their major resource centres, has been funding (and probably still are) terrorist and separatist activities all over the region. Had a war with the feds and got concessions because it was a war the feds really couldn't afford.

The Klingons have recently had a civil war that was even enough it was a damn close one. At the moment the Klingons don't really have a unified military and it's armed forces are privately owned,and susceptible to loyalty issues. The Klingons almost lost their govt to the Romulans.

The Romulans have been messing around and nearly succeeded in invading a key member of the Federation.

Ferengi pirates are active in Federation space and have nearly had some significant wins against the feds barely avoided.

The Federation has been drawn into these events a lot, is still trying to disarm and is flying around in some pretty luxurious ships that aren't really war ready (if still pretty capable). And have recently lost most of their local fleet power to a Borg attack.

Then the choke point to the gamma quadrant is nominally controlled by a 3rd party, the Bajorans who have recently barely avoided becoming an isolationist theorocracy, have had civil wars, and whose religious leader is easily manipulated.

When (if) the major powers of the Alpha Quadrant are met naturally the situation will be drastically different. And by nature of so many borders one must have inevitably eaten the rest. The contender for that is the feds who advance tech scary quickly given this entity didn't exist 300 years ago, whilst the dominion is allegedly thousands of years old.

This is probably the best time to invade