A pilot reported loss of GPS signal and a Terrain Alert Warning on departure.

Narrative

During the initial climb on the ZZZZZ2 RNAV departure off of runway XXL; we had a TAWS (Terrain Alert Warning) and a GPS lost warning. We also lost all GPS navigation guidance to the Autopilot. I took over by using the heading mode while informing ATC departure control that we had lost all GPS signal and requested Radar Vectors. I was given a Radar Vector to a heading of 140 degrees and instruction to remain clear of all obstructions. I also asked ATC if any other aircraft had experienced the same issue. The response was negative. Since; I had a second pilot; I instructed them to check the GPS integrity and satellite strength. While they were performing the task; I continued to fly the aircraft and communicate with ATC. After approximately three minutes after losing signal; we regained GPS signal and the second pilot confirmed system integrity. I subsequently informed ATC that we had regained GPS navigation ability and they eventually cleared us direct to a navigation fix and I reengaged the GPS navigation mode without any further problems to our destination.