B737-700
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 225; Flight Crew Type 225
Workload; Time Pressure; Situational Awareness
ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
Flight Crew Overcame Equipment Problem
Human Factors
Long flight from ZZZ to ZZZ1; dropped into a very busy approach sector. Weather was 1800 overcast; and the RNAV to [Runway] XXL was programmed in the box. The brief was to be below the weather at the FAF; and do the visual backed up by the RNAV. Tailwind from the west for descent. It was a very busy sector and the Controller overshot us to the east on final and gave us a 330 vector to get back to final. Once on final; the Tower had said we would break out at 600 ft; which I could see as a scattered deck. I reset the minimums before the FAF and started down. When I broke out of all the clouds; I could see I was low on [the] glidepath; and I leveled off to intercept the glidepath and landed. Tower gave us a check altitude call; as I was in the process of correcting.What I should have done; was to realize how task saturated that segment of the approach was; realize I was not properly set up for the RNAV approach and executed a go-around and get set up properly.   With all of the vectors and speed changes; it was unrealistic to fly the full RNAV approach. We were only going to get the final approach section.  I was using Level Change to manage the descent with the tailwind.  VNAV would have worked much better to adapt to changing conditions.
ZZZ to ZZZ1. Briefed 'Visual to [Runway] XXL; back up with RNAV'. Radio very congested and descent tailwind resulted in late and slightly high turn to final for RNAV. Cleared for approach. Tower said 'cleared to land; should breakout at 600 feet' and we reset bugs to DA and noted Missed Approach procedure in the FMC. As Pilot Monitoring; I responded to FAF callout 'ZZZZZ 1600'; and we started down to DA. We broke out of the clouds and could see we were low on the VASI glidepath. I stated this just prior to ZZZ1 Tower making a 'check altitude' call and the First Officer was already making a correction. We resumed normal glidepath and the remainder of the flight was uneventful.As Pilot Monitoring; I was distracted by the unexpected low ceiling and did a poor job verifying proper mode selection and monitoring expected descent rate. I should have directed a go-around; at the realization that we were in Level Change and not VNAV.
Air Carrier flight crew reported receiving a low altitude alert from tower during visual approach while in the process of correcting to glidepath.