Petunia seedlings grow slowly. I have to start mine in February to get them ready for the June 1st planting.
I use peat pots to start my seeds. I like to use peat pots because it keeps me from disturbing the root systems of the seedlings. The roots grow firmly into the peat pots. I just pop the peat pot into a larger container of soil and let the the roots grow out of the pot.
I let the peat pots soak in water until they are full size and moist.
I cover the seed tray with a plastic cover.
Petunia seeds need light to germinate. I use three levels of lighting so I don't cook the seedlings as they emerge.
At initial planting, I put the grow lights about 2ft above the seedlings and give them about 4 hrs of light. I spray the seedlings with water about twice a day. When the plants emerge, I drop the lights down about 6 inches keeping the 4 hr exposure.
Every step is small and important. But the results are worth it. Good luck !!