Most important thing to learn as a gardener is that different plants have different needs / requirements.
Veggies can broadly be divided into cool weather crops and warm weather crops.
Your broccoli, spinach, and lettuce (along with cabbage, brussels sprouts, swiss chard, carrots, turnips) are cool weather crops. Starting from seed, they could have been planted some time ago. I start my broccoli indoors in mid Jan and plant it out mid march, which is a month ahead of my average last frost date. So it does go through some snow and frost. Lettuce I direct seed in the ground as soon as the ground can be worked (ie it is unfrozen and dried out enough not to clump up). It also goes through some frost and snow after that.
More or less everything else is warm weather crops. The curcurbits especially (that is squash, cucumber, melon) like the soil to be not just frost free, but warmed up some before they are planted. Probably still too early for them where you are.
But get the cool weather things in already!
It's probably already a bit late for starting broccoli from seed... If it gets hot too early, the broccoli can tend to go straight to flower without setting heads. (I'm not saying it's too late, I'm just saying do it soon!)