How long would it have been before the base-building aspects began to show? How would the players get the advanced materials needed for vehicles?
Expected time? A week, in-game time, if players sat down and set up shop and had enough droids to do it.
"Advanced materials" is a bit of a misnomer; specific materials might be used for specific things, but the majority of stuff would be synthesized by the droids or manufacturing plants. The universe is based around using "whatever" as a construction tool. The higher density of the material, the better, and sometimes a heavy metal would be needed or a chemical would be necessary, but the droids would be able to harvest anything, and if the chemical was naturally occurring it would be a simple matter to acquire it.
Building is heavily reliant on A.I.; so much so that the first building, the Base Headquarters, has the primary purpose of housing the A.I. for the base (and, well, producing basic rations and more droids). From that point, it builds blueprints for other buildings through extrapolation of necessity or observations.
(The universe is a brainchild of mine that was originally meant for an RTSFPSRPG. Fully functional real time strategy (including A.I. controlled units and turrets), total first person shooter (including weapon swapping, weapon dropping, loadout customization, vehicle driving), and some parts of an RPG (but not to the extent of a new player having no chance against a veteran player; it was my thought that level 100 should be twice as strong as level 1.) I kind of lack every means for turning it into a reality, but adapting it to PnP is not an impossible feat for one layman.)
As an aside; I have actually been thinking about a game in a different direction in the same universe. One highlighting the most interesting feature (at least as far as I think); everything is customizable and redesignable. A gun doesn't necessarily fire bullets; it could fire shells or flechette instead. It could even be set up to fire any of the three, or have cartridges that can be fired differently depending on the gun's setting.