RE: XPS 13 9360 - first half-second of any sound is missing from USB-C/HDMI
I'm the OP and this is my update with a final resolution at the end.
To help me narrow down this problem I bought another laptop - an HP ENVY x360 with Intel i7-7500U CPU and Intel 620 Graphics. (Dell 9360 has Intel i7-7560U and Intel 640 Graphics.) The HP has an HDMI port in addition to USB-C, so I connected to the monitor with a regular HDMI cable to rule out any USB-C-to-HDMI conversion issues. The HP laptop has the same problem as the Dell. I put myself through a couple of long sessions with HP support; they offered the same things as Dell: update to latest everything, including BIOS. Try latest not-yet-approved-by-laptop-vendor driver direct from Intel. Reset to original factory software load. These steps did not help with the HP laptop either. At this point the HP support guy just gave up. "I don't know what to tell you," he said.
To review, the problem is present on both the Dell and HP laptops. I have two other computers, a Macbook Pro running Windows 10 in a virtual machine and a Windows 10 desktop, that I can connect to either of two HDMI monitors and the problem is not present.
This narrows down the problem to Intel Graphics. The same driver is used for Graphics 620 (HP) and 640 (Dell). If the problem can be solved at the driver level, it will be fixed if or when Intel chooses to.
In the meantime, I am thankful that I bought both these laptops from Costco. (Actually, I make that choice deliberately whenever possible because of their return policies.) I returned both laptops, and got a full refund. I am out "only" about $60 for all the cables I bought, and some hours of my time.
Final resolution? I have gone back to using my old Macbook Pro laptop running Windows 10 in a virtual machine, which does not have this audio problem.