I think most of them take week to 10 days to hatch from newly laid eggs, but I have looked it up. The one in your photo is actually a butterfly BTW -- Cabbage White. They have velvety frosty green caterpillars that blend in well with cabbage and broccoli leaves, but typically they are along the edge of a hole they are making or the center rib of the leaf.
There are two types of moth larva that I get on my brassica -- cabbage looper and cross-striped cabbageworm. Cross-striped is by far the worst out of all three of them because the eggs are laid in a cluster of tiny yellow wax-like smear, then they all hatch at once and start munching at once. I agree they seem to prefer broccoli to cabbage (and sweeter kale like Dwarf Scotch to Red Russian). The moths fly and lay their eggs at night.
HGIC 2203 Cabbage, Broccoli & Other Cole Crop Insect Pests : Extension : Clemson University : South Carolina
https://www.clemson.edu/extension/hgic/p ... c2203.html
BTW, I saw My snake yesterday, too.
...yeah radish is harder because of the fuzzy/prickly leaves. But they don't like it much either, I think? I pick them off when they are big enough.
And the NEAT guy is a juice sucking leaf-hopper. Not too bad except sometimes they transmit diseases. Look for spittle bugs -- bubbles of spit-like hiding place on stems where their larvae hide.