A 2012 Mini won't have HDMI 2.0 support.
It should have either HDMI 1.2 or HDMI 1.4 support.
I'm thinking "1.2" -- I looked on everymac.com and it doesn't say.
This probably won't matter with the connecting cable you use.
It MIGHT matter depending on what the display/tv can "recognize".
My suggestion is to use the cable you have.
If the tv has multiple HDMI inputs, try each of them.
What results do you get?
An acquaintance brought the mac mini again with complaints that it was working very slowly and that the TV was being set up. I gave a link to this site, but once I applied again, it means that I was hesitating to register. Anyway.
What we have:
1) when connected to HDMI port 1 and 2, there is an image, sound, mac mini automatically sets the resolution to 720p. However, the TV itself cannot correctly recognize the scene, and in the menu the machine every minute tries to select the following scenes: "movie", "priority of the game", "priority for viewing photos, refresh rate 60Hz", "viewing graphics". Because of this, there are methodical frame breaks with the output of information that the TV has changed the scene selection mode (a black frame with an information menu about the change of mode is visible). Computer mode is not available.
2) when connected to HDMI ports 1 and 2 using an HDMI cable from PS4, there is an image, sound, mac mini automatically sets the resolution to 720p. When I turn on the computer, a purple screen appears for a couple of seconds. After a couple of seconds, the color is restored.
3) I found another HDMI wire in the bins - a black braid with gray plugs, without any designations. Copper braid. When turned on, only a welcome sound is heard, there is no picture.