Growing cucumbers and zucchini for the first time and having trouble.

I sprouted some zucchini and cucumber seeds a while ago and the zucchini are doing great, but the cucumber sprouts keep wilting and dying. Not sure if it's the heat, or if I'm over-watering them, or if they need to be planted soon in deeper soil. Any tips? Also, when I plant them (they're in those cardboard cups rn), planning to do so in plastic crates on the balcony of my apartment. Any suggestions regarding soil depth/type for doing that?