I’m not much of a fan of Wookieepedia apart from using it merely for reference, but

https://starwars.fandom.com/wiki/DS-2_Death_Star_II_Mobile_Battle_Station#Construction

does do a half reasonable job at explaining the construction of it. Nearly as good as Channel72 has in here!

One thing I do very much like from their description, coupled with Channel72’s reasoning, is that:

"The construction of the Death Star II was conducted in four main stages. The primary stage focused on assembling the components necessary for construction of the reactor core as well as the two massive cylindrical polar columns used to distribute power around the station. With the main power systems in place, four reactor shafts were then fixed to the reactor. Next, a polar cap was fixed to the free end of each polar column, and subsidiary shafts were added to the columns and the four reactor shafts. The equatorial, or “waistband,” regions were then constructed, as they contained important docking facilities and the ion thrusters that rotated the station. The third stage prioritized construction of the superlaser. After the main weapon’s completion, construction efforts were then focused on the station’s outer shell and inner levels, including the Emperor’s tower, which was anchored to the station long before his arrival.

As was confirmed during development of the first Death Star, construction advanced most efficiently when the working surface allowed for sufficient space for the greatest possible number of self-replicating construction droids. This was Moff Jerjerrod’s justification for filling the inner structures in a piecemeal manner."

The 4 stages breakdown, and the piecemeal manner of filling in the inner structures later does lend an air of believability to how it could be constructed so quickly, with the reminder it was not anywhere near finished as we saw on screen. Along with the surprise that the super laser was in fact fully operational, and that this was part of Emperor’s plan to lure the growing rebellion out.