How are you growing outdoors? Pots? Raised beds? In the ground? I grow in raised beds and I've put my seedlings out as young as 10 days old at the end of April. This is what they look like now:
The first pic is the best I have of everybody--even the veggies, sorry!-- and the second is of the actual seedlings that were only 10 days old when I put them out on April 28 this year. They went into pots first in case I had to protect them from cold, but the pots were sitting right where the plants are growing now. I never transplant more than twice: seedling germinated in peat pot, transplanted once to pot, usually within two weeks or so, and then transplanted one last time to their beds. Yeah, everyone is kinda ragged and what-not. I'm lazy and pretty much let them grow as they wish
The netting you see on the laths is to keep the area feral cats from turning my beds into litter boxes. So, get them puppies out into the sun!! After you give them a few days of shade and dappled sun first so they don't fry
But get them out of those pots into something much bigger and let them stretch their roots. Happy growing!!