I still don't understand where sand came into the discussion either, the OP indicated "double plastic cups with soil."
@Maple11 , if you literally meant "soil," as in garden soil or whatever, I would suggest using a regular potting mix instead. Also, buying a packet of the type of seeds you want to grow would be more reliable than using any type of store-bought tomatoes.
After 4 weeks your seedlings will likely still be quite small, as well as the beginning of April seems like it might be early for planting in your area; wait until you aren't expecting any more freezing temps before putting the plants outside. Be sure to give your plants plenty of light while they're indoors so they don't become "leggy" and weak, and once you move them outside you will need to gradually acclimate them to the sun and wind.