Thanks for the additional information!
I checked HP’s product page for this system and it does not specifically state support for USB-C Video output which likely means this is not enabled on this system ( USB-C DisplayPort Alternate Mode is the current standard for outputting video over USB-C and Thunderbolt 3, this is an optional feature that has to be specifically enabled by the system manufacturer ).
This system should work well with our UD-3900 USB 3.0 Dual Display Docking Station ( https://plugable.com/products/ud-3900 ). Alternatively our USB3-3900DHE USB 3.0 Dual Display Adapter for Multiple Monitors with Gigabit Ethernet ( https://plugable.com/products/usb3-3900dhe ) does not provide the additional USB ports, nor does it require an external power supply. This adapter will drive both displays, one can be connected directly to the adapter’s HDMI output while the other will need a DVI-to-HDMI adapter or cable ( available from Amazon or other retailers ).
Both the docking station and graphics adapter require the DisplayLink software to be installed on the system, available from our website here ( https://plugable.com/drivers/displaylink ). We recommend DisplayLink based USB graphics adapters and docking stations for use with office and web browsing software, displays on the DisplayLink device may not be well suited for full screen video playback, 2D or 3D graphics software, video editing software, or some stock trading applications. We do not support gaming on DisplayLink attached displays.
Please let me know if this helps, or if you have any additional questions.