I have an EliteBook 840 G6 and a new HP USB-C Dock G5. I replaced the TPA-B01 docking station where I had this same problem but the problem remains:
When I turn on notebook from cold start, the dock will mostly work (display, ethernet) but USB will not work through the dock and the dock does not show up in Device Manager. If I unplug and replug USB-C cable to dock, everything works.
If I restart without power down, I will not lose recognition of the device and USB connectivity.
If I sleep from the dock button, I will not lose recognition of the device and USB connectivity.
However, every morning when I boot up, I must disconnect and reconnect the dock to get my USB devices.
I have updated all drivers including BIOS and dock firmware and still have this problem. As I pointed out, I had the same problem with the older dock. I thought since it is now unsupported I needed to buy a new dock which I did, to no avail.