It is not on the VMware compatibility list, so it is not supported. May it work? Maybe, but this is not guaranteed.
What is the model/vendor of the network card? Anther option would be to install VMWare Workstation on it and do nested ESXi, mostly used if you want to play with ESXi or a test lab.
Since it's not on the compatibility list, you can't use an HP custom image.
Use the ESXi ISO from VMware.
HPE builds of ESXi are only for ProLiant servers, nothing else, and definitely not HP desktops.
The only thing related between ProLiant and desktops is their stock ticker symbol. Other than that, they are two wholly different species.
You will have better luck installing a regular vanilla build of ESXi, the same what every other whitebox server must use, and play the game with the Physical Adapter compatibility list.