There are at least two, and perhaps as many as four ways to remote release a Z7 (presumably a Z6 as well) besides the self-timer (which works just fine, and is my usual method).
If it's paired to your phone, SnapBridge has a shutter button, which works reliably (it's WiFi, so the range is pretty good, and it works from any side of the camera). I've used this, and it works.
It does have a remote socket - it's just not the one you're looking for. It takes Nikon's MC-DC2 remote (like the consumer cameras) rather than the pro-style 10-pin remote. I've never used it, but it's the odd little socket under the HDMI port. Plenty of cheap alternatives to the Nikon cord, some with intervalometers and the like. There are also radio triggers that fit that port.
It may well also fire from the USB port and/or the mic jack - many cameras do... I haven't tried either one.