I'd say that is your best bet, I tried various hubs/adapters with my 16" to USB-C > DisplayPort and while they seemed to work just fine freesync was grayed out with my Phillips 436M6 that does support Freesync. It also did not work via direct USB C > USB-C input which this monitor has. A Plugable brand USB-C > DisplayPort cable from Amazon was what worked for me. So i'm not sure the standards or requirements for it to work with HDMI but a basic cable is what ended up working the best for me.
I recently got an ASUS VG245HE external display, to which I'm hooking my MBP 16" for various usages. I see it supports Freesync, but option is grayed in the AMD settings.
Is Freesync just not supported?
Currently using MBP 16" with 5500M 8GB.
You can also check if your external display has any firmware updates on it's online support page. Some displays actually do have these and you update them usually by putting the firmware on a USB stick and plugging it into a USB port that's in the monitor