Good question, Altuve (in Florida):
The answer is complex, but here's a few simplified, applicable principles:
1. For the majority of wood-warbler species in the Lower 48 of the USA, an initial clutch of newborns has already occurred.
Likewise, a good percentage first-year individuals have already dispersed from their natal nest origin.
This behavior may include foraging nearby where they were born, but not yet migrating by night to a non-breeding, "over-wintering" territory.
2. Which species are early dispersers (and migrators)?
In the West where I live (in the San Francisco Bay Area), Orange-crowned Warbler has completed its nesting cycle. Both young and adults have dispersed elsewhere, including (in some cases) to higher elevation "intermediate" staging areas where foraging opportunities are more successful where larger blooms of insects remain robust compared to the dry, often hot weather in non-coastal Bay Area locations.
In many cases, true southbound migration will follow by August and September.
In the East and Midwest, early dispersers include Tennessee and Yellow Warbler. By late July and August, I have periodically seen banders nets hosting these two species in areas where they do not nest.
3. As for more peak periods of warbler migration, it's fair to suggest that August and September are more common to note larger pulses of many other warbler species during the day as they forage before migrating at night to areas that range from southern states to Central America.
Then again, in my area, we welcome back a plentitude of Townsend's Warbler individuals by September and October as they return for the non-breeding season from more northern latitude breeding grounds.
I hope this explanation helps.