Seeds too deep?

Germed 6 seeds in paper towel on 4/20. 5 days later 5 seeds had sprouted placed them in peat cups w/potting soil then submerged peat cups into ground in my veggie garden. Holes already prepped at another location for their eventual summer home.
Problem- once I watered the potting soil (after peat cups were in the ground) the soil compacted leaving 1/4" or so of exposed peat cup, during a hard rain a couple of days later each peat cup filled to the brim with soil from my veggie garden and is now a rather thick mud instead of the nice loose soil I would prefer to have. This also made my seeds deeper in the dirt than planned. I may be seeing something popping though today in one cup but am not sure. It has been 8 days since planting and had hoped to see more above ground growth by now. Also days have been rather cool and lots of rain, good drainage though.
My presumption is all I can do is hope for the best, wait and see that if it is the nature of the seed to grow. But how long should I wait? Or could all the moisture and the caked on mud cause the seeds to rot?
Any comments from experienced growers would be appreciated.

If you have more seeds left I would plant another seed in each cup. But if so much water rose up during the rain that it caused soil to float up over the rim of the cups I would have to wonder whether it's actually well drained, aerated soil. Sounds like you had a puddle in the garden. We've had the same thing where I live, a town not too far had severe flash flooding. :(

Put a little soil in the peat cups but don't bury them till you have about 6 inches of growth. Just a couple flakes of soil is all you need to germinate and use a spray bottle to keep the soil moist. If they get soaked the seeds rot.