The official NVMe hat blocks access to the PoE header, but there are third party options that combine NVMe and PoE into one hat:

https://www.youtube.com/watch?v=x9ceI0_r_Kg

Alternatively you could get one of the NVMe boards that sits under the Pi, and put a standard PoE hat on top.

The Pineboards PoE + NVMe HAT will be released next week and will allow you to have both, and some other 3rd party ones do the same. The official Pi M.2 HAT does block the PoE headers though sadly!