ASRS 2062528

We were an hour late on our schedule after a late passenger and deicing in BJC so had to quick turn at ZZZ to repo to TEB and get the aircraft serviced before a late flight with pax back to ZZZ. Descending out of 15000 into TEB we got a divert message to BWI. We managed to get the divert accomplished but when cleared for a visual for 33R they asked us to turn inside of 5 miles so I began my base turn at 4 miles while configuring, hand flying and trying to reference the runway visually (the PAPIs were dim and indistinguishable) so I referenced the displayed glide path and began my descent out of 2000 (FAF altitude) and lost the runway as I was cross checking the PFD and map. Tower gave us a low altitude alert and I immediately added power (flaps2 and gear down) and began a climb out of 1400 feet. I was able to reference the runway again and we were low and I suspect I had a false glide path and was too far to the right of center line to get accurate indications regardless. The rest of the approach was normal. I am realizing we go from delay to massive schedule compression without taking time to take a breath, sit down and eat, and accept diversions at transition to night without considering the risks. I intend to be more disciplined in the future and pad these events with the time I need, either asking for a full approach at night or calling in to delay a departure.