Summer is a bad time to sow seed in hot climates. Many plants go into a kind of dormancy when temps are high, even if they have enough water. You could speed things up by sowing in late winter/ early spring. My late sown peppers usually flower 6- 8 weeks after sowing and peppers start to form a few weeks later. I find they crop better though when sown in late fall, when it is still pretty warm, so germination is good, then grow fairly slowly over "winter", which is not very cold here, to flower and fruit late spring to summer. That way they also withstand drought better. Plants that are allowed to develop more slowly are often more robust. I used to grow Alyssum in England and I would think that would do best in the coolest possible conditions.