Air carrier Captain reported descent below glide path caused a Ground Proximity Warning.

Narrative

We were cleared direct to ZZZZZ; a fix on the ILS XXL descending to 3;000'. The aircraft then leveled at 250kts at 14nm from Runway XXL. We were subsequently cleared for the Visual XXL. We set speed to 200kts and at 13nm slowing through 215kt called for flaps 1. Speed was set to 190kts and at 9nm slowing through 200kts called for flaps 2. The speed was set at 170kts and the Altitude Selector was set to 2;800' to allow the aircraft to initiate the descent in FMS path before capturing glideslope; however the aircraft captured the localizer but the glideslope was below our altitude at the final approach fix so the aircraft defaulted to FPA (Flight Path Angle) and began to level at 2;800'. As the pilot flying; I disengaged the autopilot and flight director and began a descent to capture the glideslope. As we initiated the descent I called for flaps 5 and speed Vapp. Both crew members verified descent rate and the glideslope was captured. At this time the aircraft descent rate was adjusted to maintain the glideslope but the autothrottles continued to allow the aircraft to slow. The aircraft began to sink below the glideslope to prevent further deviation from the glideslope; I pushed the throttles forward to allow the glideslope to come back in while preventing our airspeed from deteriorating. The autothrottles continued to require override and were then disconnected. During this time the aircraft had descended below glideslope and a GPWS aural warning GLIDESLOPE occurred. Immediate adjustments were made to the aircraft path and the remainder of the approach was completely without further incident.