What’s the best way to kill and prevent cab grads from taking over?

When you started the garden did you use of of the techniques to kill all the weed seeds in the soil? e.g. putting something like black plastic down to cover the ground for several months at least.

Crab grass in difficult because it grows from runners as well as seed. Try to get all of the roots out if you can.

My garden is small and I week like you are doing and its a chore. I remember watching Amish working in a large field and they were using hoes, not to totally remove the weeds but to disrupt them perhaps this might work for you.

In the spring you treat the lawn with pre-emergent crab grass killer. You will need a lawn spreader to do this. This will keep it from coming up. After it's up, it's pretty impossible to kill without killing your grass. It's an annual, so it dies out every year.