Why are you starting it inside? Garlic is one of the most cold hardy plants there is and starting inside, especially under lights is not only un-necessary, but asking for other problems associated with daylight sensitivity.
If you're ground is still frozen, put it in as soon as you can work up the soil and it'll be fine.

I would also advise against starting it indoors. Have you checked to see when garlic is usually put in the ground in your area? How long was your garlic in the ground? I'm in Texas & it's planted about mid-October & harvested in late spring. It's my understanding that garlic grows its roots over the winter months & the bulb part grows mostly when the weather warms. The bulb benefits from the long roots that grew over the winter.

I don't think Garlic would transplant O_o? I have grown Garlic indoors over the winter but only for the chives and something pretty growing indoors :) But I have never had any luck actually transplanting it.