An air carrier First Officer reported they descended below the glidepath and Tower issued a low altitude alert.

Narrative

I was pilot flying in approach to RWY XXL was normal until we intercepted the localizer. Glide slope appeared to be below us so I started to use the vertical speed down after setting a higher altitude than we were; per procedure; to catch the glide slope. The tower issued a Low Altitude Alert; and I realized we were not on the glide path; so I clicked off the auto pilot and pitched up until it looked normal visually. I asked if we should go around; and the Captain said it wasn't needed. Captain asked the tower about the glide slope; and the tower said it was NOTAM'd out. Went back to normal glidepath and landed without incident. Cause: Wake up calls for the whole trip were early hours; so we were both quite tired after a lot of flying. I neglected to look at the NOTAM's carefully; as the GS was NOTAM'd out. The runway had no PAPI; so the visual clues were decreased. The Captain listened to the ATIS alone; and I should've been listening with him or checked it myself. Most cities have Digital ATIS; so that was not an option to look at the JEPP ATIS. I should've just hand-flown the approach visually; but I always start with the ILS if there is one; to make sure I land on the correct runway and airport. I am a bit hesitant to hand fly the airbus as it is quite automated; but should probably practice doing this more. Next time I will ask the Captain to look outside and tell him I am setting the altitude higher to use vertical speed to get to the glide slope. Or; perhaps not use that procedure at all; as it has no bottom if the GS doesn't catch you. Of course; had we realized it was NOTAM'd out; I would not have done that at all. When we realized we were too low; I should've just called go around" and come around for another one. Something was wrong; and we needed to reset everything and regroup. The go around procedure is complicated; and I might've been hesitant because I don't know it as well as I should. I also think the tower should advise us that the glideslope is inoperative when clearing us to land. They probably assume we don't use it on a visual; but of course that's not true. Suggestion: Both pilots should always listen to verbal clearances and broadcasted ATIS reports together. I should've looked outside more; and not fixated on getting the automation to fly the approach properly. I should practice hand flying more on visual approaches on clear days. I should call go around if anything went wrong; even if it appears the problem is fixed; and we are prepared to land."