Depends on the strain, and in my opinion, it takes longer than 2-3 weeks to show. During the 2-3 weeks time, buds hardly form on the plant, instead, the top stretched upwards during that time.

I'm guessing anywhere from 4 weeks, you should see the start of trich production, but if it is a poorly grown plant, then the trichs will be lacking. Some strains carry tons of resin/trichs, while others don't pack as much.