I do this with proxmox on a Lenovo tinypc. However I’m using a Nvidia gpu for passthrough. Was awhile ago I set it all up. I remember it being fairly complex. Here is a super basic instruction for it. Possibly incomplete.

Check you have iommu enabled in efi/bios. (For Intel - enable vt-d)

Install drivers if necessary (again nvidia)

Blacklist device on proxmox host

Setup GPU passthrough (vfio) - assign the card video and audio to the guest vm.

Start vm and test

If you are using onboard card, you can probably blacklist it and use it for your vm… I’m not entirely sure how proxmox deals with losing its primary display… I expect it’ll cope ok. SSH for everything. Probably need to use virtio drivers. Install within guest…