The primary things that kill seedlings are too much water, soil too compacted and roots rot, too much fertilizer, too much surface moisture and fungus grows. If you have well draining soil and some airflow around the plants then the water and fungus issues are largely avoided even if you overwater. If your plastic seedling tray has a clear top as many do, leave the top off for at least a couple hours if you see moisture accumulating on it. Once you have sprouts poking out of the ground, then I'd not use the top at all anymore.