Eclipse 500 Captain reported a CFIT event during final approach that was caused by descending below glide path. The Captain corrected back to proper glide path and continued to a safe landing.

Narrative

On downwind prior to ZZZ visual approach to Runway XX I briefed that we would need sunglasses on the approach as we turned to face the sun low on the western horizon. As the majority of the flight was eastward; I had forgotten that my sun visor was MEL inoperative and unusable. All normal until turning to cross the shoreline heading west into the harbor mouth at approximately 1500 ft. MSL with the runway; ZZZ in sight. In the ZZZ on the approach path; the sun was directly ahead and was more intense than I had expected. In the momentary distraction reaching for the sun visor and remembering it was not available; vertical speed increased to 1200 FPM around 1100 ft. MSL. The First Officer (PM) reported that I was descending below glide path and I started the pull up to recover normal glide path. ZZZ Tower reported an altitude alert to us. This was quickly followed by an Enhanced Ground Proximity Warning System (EGPWS) 'Obstacle Ahead' caution for the bridge ahead of us and a Pull Up; alert. With the bridge clearance assured and climbing to the normal glide path; I followed the right bend in the visual approach over the harbor; away from the sun; and recovered the normal glide path (PAPI) above 600 ft. AGL. The approach was stable at 500 AGL. The First Officer asked ZZZ Tower if we were still cleared to land. ZZZ Tower responded that we were still cleared to land. The rest of the flight to landing and the arrival gate was uneventful.