Neither the Garmin connect app or Garmin express firmware updates to my new fenix 5x. I can sync my steps with my phone, and Garmin express downloaded updated apps. However neither are pushing software or firmware updates.
How new? you might be up to date already? Do you have with wifi address setup for the watch, I think the firmware auto-updates are via wifi, not bluetooth. But I could be wrong on that.
Check in about to see what version you are running. If it's an APAC version of the watch, the FW number may be different than what is commonly talked about here with a "Rest Of World" device.
Also, if the last digit of the FW is 0, it's production and you get those automatically. If it's not 0 (11.57 for example), you must manually install that beta FW. So if you're expecting 11.57, see that thread and the instructions to install it. (Betas are only available for ROW devices)