Air carrier flight crew reported while on a visual approach they descended below the glide path resulting with ATC issuing a low altitude alert and flying towards terrain. The flight crew rejoined the glide path and landed safely at the airport.

Narrative

During our approach into ZZZ; the First Officer (FO) was flying the aircraft while I (Captain) was monitoring. We were following the visual approach to Runway XX; and ATC instructed us to maintain 170 knots until 5 nautical miles (NM) from the Runway.During the arrival phase; we were cleared for an unrestricted descent to 2500 feet. The FO ( pilot flying) selected level change to manage the descent. Approximately at 3000 feet; we received a vector to intercept for our approach. Pilot flying selected. L-NAV to fly direct to ZZZZZ (IF) and then engaged V-NAV; to which I (Pilot Monitoring) saw the FO pressing the button but did not confirm the engagement with the Flight Mode Annunciator (FMA). First Officer missed double checking VNAV activation because he was trying to get configure to flaps 40 while ATC had requested 170kt till 5NM.The FO set the altitude to 500 feet; which was immediately corrected to 600 feet by me to ensure it met the Minimums (550 feet).As we continued descending and configuring the aircraft; we were running the landing checklist. I was heads down while the FO was flying the aircraft. At around 900 feet; ATC called our flight number and followed with a low altitude alert. Shortly thereafter; a GPS Warning (GPSW) alert appeared. The FO had disengaged the autopilot and leveled off the aircraft at this point.ATC instructed us to continue the approach and expect landing clearance short final.At all times we were in visual conditions and were able to continue the approach safely. I noticed that VNAV was not active; so I worked to re-engage VNAV and ensure proper vertical guidance. We received landing clearance and successfully landed at ZZZ.Cause: The landing checklist and aircraft configuration tasks led to a temporary lack of situational awareness regarding altitude and VNAV status. The original FO reported fatigue due to extremely loud conditions at the hotel the night before; and while I (Captain) did not specifically call out fatigue; I also did not have a good night's sleep; which may have affected overall alertness and performance. The busy nature of the ATC workload; particularly with vectoring and managing multiple aircraft; may have contributed to the timing and frequency of instructions and alerts; potentially affecting our response and situational awareness. With ATCs request to maintain 170kt until 5NM; getting configured was a worry both pilots had. Upon noticing VNAV was inactive; I promptly worked to re-engage VNAV and ensure proper vertical guidance. We maintained visual reference and continued the approach safely; leading to a successful landing.Suggestions: Complete checklists and aircraft configuration tasks with minimal distraction and ensure continuous situational awareness; especially during critical phases of flight. Autopilot and VNAV Monitoring: Ensure proper engagement and monitoring of autopilot LNAV and VNAV systems to prevent altitude deviations and potential alerts. Maintain awareness of minimums and approach altitudes throughout the approach phase to avoid altitude-related alerts. Address and mitigate factors contributing to fatigue; including ensuring adequate rest and reporting any fatigue-related issues that may affect performance. Consider enhanced coordination and communication with ATC; particularly during busy phases; to ensure clear and effective handling of instructions and alerts. The approach and landing were completed safely despite the low altitude and GPS warnings. The prompt re-engagement of VNAV and continued visual guidance by pilot flying ensured a successful outcome. Addressing fatigue; improving alertness; and managing ATC workload can further enhance overall performance and safety.