I've been starting from seed for over 20 years.
A couple things that increase successful transplants. You absolutely have to "harden off" the seedlings.
I mix soil from the garden at a minimum 50/50 with peat/ sterile soil. I used to sterilize the garden soil by baking or boiling, but the few that die from "damping off" weren't hardy enough to survive anyway.
I supplement 14 hours of grow lights with taking the seedlings outside at every opportunity. It takes a little extra work, but direct sunlight gives off a wider spectrum of light from infrared to ultraviolet that the grow light s lack. Wind, rain, cold into the 30s (bring them in before it drops below freezing) and heat produce hardy, stout little plants that are easily transplanted into the garden.