I started them indoors in the summer a couple of years ago so I could transplant them into the fall garden once the weather began to cool off. Mine started to get a little leggy because indoor light just isn't a match for outdoor light, so I potted them up from the cells in the 72-cell starter flat into 5 oz. paper bathroom cups. When I potted them up, I set them as deeply into the growing medium as I could, burying some of that leggy growth in the soil-less mix and they grew just fine. I transplanted them out into the garden about 10 days later after hardening them off. So, I think it is likely you could do the same if you choose to repot them.

On the other hand, it is still pretty early and the temperatures still are pretty cold, and beet seed sprouts easily indoors, so you have plenty of time if you want to start over with another batch.