The size they are in now looks fine. (for now) Tisn't a catastrophe using those pots...just a pain.
I start in a 2-cup pot, then 1 gallon, 3 gallon, and finally to a 5 gallon pot which takes me thru harvest. (all of 'em are plastic)

Water them so all zones of the soil gets moist when you water. Add half the water you intend on giving, then a few minutes later add the rest. This allows soil to absorb the water rather than it finding a quick path out the bottom. Then let the soil dry till next watering.
In a couple of weeks, start the nutes. (half-strength, observe the results) Eventually, (likely a couple of weeks) you'll work up to a full-strength mix once they acclimate.

So how are your youngsters looking now?