With only one PCIe slot, your options are limited.
Could you check what HP support says?
Expansion slots
Note: The configuration might vary depending on your model.
Do you only have one PCIe slot, or two PCIe slots, one of which is already occupied?
Anyway, with only one PCIe slot, you'll have to use it for the USB-C DP Alt Mode card.
Your HP desktop has an HDMI 1.4 port, you'll need an HDMI 1.4 to DP 1.2 cable, for example the BolAAzuL, see https://dancharblog.wordpress.com/2020/05/10/bi-directional-usbc-dp-cables/#hdmi-1-4-dp-1-2-cables-adapters-single-direction for more info.
For DP 1.2, you'll go for the SUNIX card. The circle is complete. Back to your original idea.😃