Your squash plants will do very well outside now that the soil has warmed . You've given them a very good start in life.  However, you can certainly grow squash indoors.  You need a large enough pot, plenty of light, a bush type (not vining) plant and a way to water the soil without wetting the leaves.   The pot should be 24 inches or more across and at least 12 inches deep to give the roots enough room to function well.  Bigger is better, squash is less likely to dry out in hot weather with more soil.  You have yours under a grow light.  You may want to leave the light on 16 hours/day to give enough light to grow the squash.  Grow lights are great, but the light is not as intense as sunlight.   Bush type squash plants work much better indoors than vining plants that require trellising and are harder to manage.  Squash plants are large plants.  Wetting the leaves of squash while watering can lead to disease.  Find a way to water only the soil, maybe a soaker-hose type ring or bottles inserted into the soil.