According to the R1 trailer, the Empire seems to have gone in the reverse order when building the first Death Star (as compared to the second one in ROTJ):
- DS1: the entire battle station is actually built first, and then the Superlaser focusing dish is placed at the completion stage.
- DS2: the Superlaser dish and the surrounding area are built first, the rest remains +/- unfinished.
Interestingly, the finale of ROTS (though I personally prefer not regard the PT as canon) shows a DS1 superstructure with the superlaser dish skeleton already in place.