A220 Captain reported due to limited visibility and aircraft limitations; a GPWS warning was received on short final that resulted in a CFTT event.

Narrative

Upon arrival the weather was VFR with visibility 10 miles. On the left downwind for the ILS to XX the approach controller asked us if we could accept the visual approach. We both had the runway in sight and I told the FO I was OK with it as long as he was. He agreed to take the visual. I then accepted the visual approach and told the controller we would turn final just outside the FAF. The controller said that would be fine; and asked us to keep it tight to the FAF. With this I warned the FO that the A220 flight director/AP (Autopilot) is not good at capturing the GS close in and to be prepared for that. We began the base turn about 1 mile outside the FAF. As we did the visibility was not as good as there was a smoky haze that the sun was glaring into as we changed our direction. Despite this we could see the runway and entire area throughout the approach. We configured accordingly. At some point the FO clicked off the Auto Pilot and hand flew the approach. As I suspected the flight director did not capture the GS immediately; eventually it did capture. Despite this we were on speed; configured; and stable at 1000'. During the last 200-300' we started getting low on the GS. I called this out to the FO and he disconnected the auto throttles and began correcting. During this we got a Glide Slope GPWS alert". Being so late in the approach we continued to a landing on runway XX. The touchdown was a bit firm but otherwise uneventful."