If you're past your last frost date, you should be fine. Some considerations:
Cooler temps mean slower growth intitially, this may not be an issues if you're trying to get a head start and have larger plants come harvest time.
You may start your plant flowering early if it matures too quickly.
It would really be better to start them indoors or some other warm place at least until you get them established. You don't know how many seedlings I've lost in my life to rabbits, squirrels, mice, bugs, harsh weather, the list goes on. They will be helpless little babies out there all alone. It's a cruel world out there, give them a good start and you'll be rewarded.