Does Europe have a ALC, or does everyone come to the states for that?

To my knowledge no ALCs are located out the United States. However the Army Reserve-Puerto Rico School House trains Soldiers at the local Bureau of Forensics Sciences. Not sure if they handle ALC.

ALC and SLC are run at the same schoolhouse where the MOS AIT is held.

Chances are you will be sent back to the States. The only NCOES I know of in Europe is BLC. I had a guy in my SLC class at FT Knox back in '19. He had to fly from Germany.