I think it will stand up again. You have almost 1/2 inch at the top of the cup. You can fill it up to the top for support and the plant will just make more roots.
I've read that the seed itself has all the nutrients it needs to get to it's first real leafs. I just start in Jiffy with a few drops of some liquid than drained from some Super Soil. The juice is really weak. It came from rained on super soil and gets diluted more.
Do you grow in the ground or pots. I would guess pots with Fox Farm. I live on a farm and have everything to make soil. I like to mix all the nutes and put them into the ground. Our native soil here is good. I just dig in a shovel full of the SS mix along with the compost. That's all they get for the year and they are very happy.