Any time, given where you're at. I grow entirely in pots for any number of reasons, the least of which is that I can easily move them in and out of cover/shelter as needed. I grew up in Houston and lived in Los Angeles for four years before moving to the frigid north, so I understand your grow conditions. I start seeds in January, due to space issues I don't start them any sooner, but we get snow here, which will kill off pepper plants pronto. You don't have to worry about that, generally, but clearly do get those random blue northers which you have to watch out for.
Keep in mind that seeds germinate best around 80F, and start them inside if it will get below 75F. After that, keep the babies fairly warm, too - try not to let them get below 60F until they're at least a foot tall. Look up hardening off, which is the process that needs to be taken to acclimate them to the outdoors when you've had them inside. Also if you have them inside, be sure to get a fan onto them pronto. This helps simulate the wind they will have outside and also helps prevent damping off. If you're able to start them outside in full sun, that is best, but if not be sure to harden them off gradually.
BTW - to clarify the terminology, in case you didn't notice the difference:
Hardening off = the process of acclimating to outdoor conditions.
Damping off = a soil fungus that will kill your plants.
Damping off occurs at the soil line, not typically below the surface of the soil. To prevent it, the two measures to take are to bottom water, ensuring the top surface doesn't get wet, and putting a fan on the plants to dry out the top faster than if there was no circulation. If a pot does get damping off, you should scrape off the surface of the soil as best as you can, and mist with a mixture of 1:10 hydrogen peroxide and water while the plants are still babies. The first sign of damping off is a softness of the stem at the soil line. After that, the plant falls over. At that point, it's likely a gonner. The fungus has a brownish color to it - the surface of the soil will be a lighter color than the soil itself, even when wet. That's part of what makes it hard to discern if you haven't seen it before. Just know that most potting soil looks almost black when wet, so if your soil looks more brown, it's probably developing the fungus. Again, good air circulation and bottom-watering usually helps immensely.