B757 First Officer reported while descending on an RNAV Approach; Tower issued a below glideslope warning.

Narrative

RNAV with VNAV had us well below glideslope.At cruise altitude; the crew briefed; the RNAV XX whiskey (ZZZ) extensively. The approach was pulled from the box; the only changes made were outside of the FAF; and were to make the altitudes at altitudes instead of at or above. I made all altitude changes with verification from the Captain; then had him independently; verify speeds; and altitudes from the start of the STAR all the way down to the runway by himself. If anything; the crew briefed more than usual; given the greater threat of Runway XX; and the fact that I don't fly normally. Eventually; the crew was given direct ZZZZZ and lateral confines of the approach. Quickly after; we were given the full approach procedure; and VNAV was engaged with the FAF altitude initially; and then the touchdown zone elevation once inside of ZZZZZ. The approach proceeded as normal all the way through the FAF. Crew configured gear early; to aid the decent; and having the at altitudes; allowed the aircraft to be lower on approach to manage energy towards the FAF. Once inside the FAF; both pilots were outside monitoring runway position; since Runway XX is notoriously difficult to see. The first indication that something was wrong was a notification from Tower that we were below glideslope. Both pilots were surprised since cross-check confirmed we were on VNAV path. Tower queried if we all had the correct altimeter set; both pilots cross checked that the altimeters were correct; then checked outside and realized we were definitely below where we needed to be. I disengaged auto pilot and auto throttle; continue to manually visual maneuver to get back on runway center line and altitude; then landed without incident.The Captain posited that because we had changed altitude on the approach; it caused a VNAV anomaly. I waited till today (several days later) to make sure I hadn't completed the procedure wrong; but I can't find anything in the flight manual; or FOM that prevents changing of altitude on the initial portion of the procedure to comply with at instead of at or above. I can't say I didn't fat finger the approach; but I would like to know what happened; whether it is the automation itself; or me making a mistake; or an interaction between the two of us that caused an error.