Challenger 300 pilot reported receiving a terrain warning after descending through a stepdown fix altitude during approach. Pilot returned to correct altitude and continued approach.

Narrative

After crossing the FAF on LOC XXR we descended too quickly on the approach course. I did not recognize the proximity to ZZZZZ so we descended through the stepdown altitude of 4060; after which a terrain warning embarrassingly (and thankfully) alerted us to this deviation. I deactivated the autopilot; returned to the profile; and continued the approach without incident. Cause: Equal parts lack of situational awareness and complacency due to CAVU conditions with the runway in sight miles prior to joining the approach. Having to join the profile from above (outside the FAF) due to ATC traffic separation didn't help with stabilization after the FAF but; but obviously that's not an abnormal maneuver; just a distraction. Not having the LOC stepdown available in the FMS was definitely a factor; but not a cause. Solution: I need to maintain more vigilance on vertical profiles of non-precision approaches. Also; having ZZZZZ and other such stepdown actually in the approach procedures in the FMS would have probably prevented it entirely; since ZZZZZ/4060 would've been presented on the MFDs. Having to rely on approach plates for situational awareness of stepdowns is bush league GA stuff. There's no reason stepdowns should be absent in the FMS like so many are. To be clear; I'm not blaming the equipment for this event; but I do think there's room for improvement.