I don’t see the + in a greenhouse underground. If you want to start seeds early, south and west exposure with big glass windows will do the trick.
A year ago we started seeds in mid January but found this was pushing us to take our plants outside too early. February 10 this time around is working well for us. All out plants are out, covered by frost blanket covers overnight.
There are some beautiful glass greenhouses on the market. Before you buy, take a critical look at where your sun light comes in and how you can take advantage of it. You may not need a greenhouse.
In Northern climes undeground greenhouse serves as a heat 'mass' to retain heat, especially in the off season.
In Southern climes , the soil mass will help cool the greenhouse , and ameliorate the varying temps by acting like a heat 'sink'.
By being underground , it is also less susceptible to wind damage , or excessive plant table drying, and helps to retain moisture in generally dry areas.