2007 BMW X5 3.0si with 4 zone climate control

Vin : 5UXFE43597L018367

No need to completely remove the belt. Disconnect from alternator and let hang. You will need to replace the (4) aluminum screws that attach alternator. If you re-use them they will break. If they break on a running engine you'll have have a real mess.

Great! Thanks so much. Yes I purchased new screws as well

I have a dumb question for the experts here - can the suv technically turn on if the battery is fully charged but there’s no alternator in the car ? I kind of wanted to test and see if my battery is okay (which is seems like it is since I put it on the charger and it said it was fully charged with 13 and something volts. Didn’t want to mess with the electronics tho and haven’t tried it

Your truck was running with w/o an alternator when battery light was on and before the battery was depleted, so it should start and run w/o alternator present. Code(s) will likely be set because DME can't communicate with voltage regulator. On some Bimmers the CAS-DME alignment needs to be re-sync'd after running or attempting to start with an undercharged battery. This is part of the X5's theft prevention system. INPA/ISTA/Foxwell can re-sync if needed.

Hmmm so is It concerning that the charger said my battery was fully charged and then I tried to turn it on with the alternator out of the truck and it didn’t start ?

I would be concerned.
To be clear when you attempt to start, the starter does turn the engine over but it doesn't start?

Yes but now that I think about it - it won’t start because the serpentine belt is off because the alternator is not in. That makes sense right ?

No. That engine should run w/o alternator belt.

Ugh okay. What do you recommend I check next?