No you need to implement a wet - dry cycle straight away, soak the soil till run off then leave it til its nearly dry, depending on your size of first pot they shouldnt need watering for a few days at least, my first seedlings i water weekly on average, first seedlings water uptake is very minimal, then as the plants grow you'll notice the soil drying up quicker as water uptake increases with the amount of leaves they have, every leaf transpires water, so more leaves = more water uptake.

1 or 2 tiny leaves = hardly any water uptake.

So, cut back on the watering and try starting in a lighter soil.