Every home / building I’ve built, I installed the door frames and trim first. I’ll pop the hinge pins and store the doors somewhere safe. Carpet is the last thing to go down, then it’s a vacuuming and move in.
Depending on the floor covering, the trim will be installed at different heights above the subfloor to give ‘just enough’ clearance for the floor covering. Typically, baseboard trim will be 3/8” above the sub floor when using carpet. As previously mentioned, the tack strip goes next to the trim, then the carpet is tucked under the trim. Seeing how you have concrete, you should talk to your carpet installer and find out if he’s going with a glue down or carpet with pad and tack strips. I don’t know how they will install tack strips to concrete though. Construction adhesive maybe? Unless the concrete is still green, nails will not hold it as even concrete nails will cause the concrete to shatter.
After the carpet is down, I go back over the trim and tweak it or spot touch up as needed. Then I hang the doors. I don’t let the installer touch doors. By that point, all they want to do is get on to the next job and usually scratch the door finish or poke holes in the walls when re-hanging the doors.
