Cold boot with the box connected to the TV and then run "getedid create" from the SSH console. It will capture the EDID data from the HDMI connection and then hardcode the HDMI connector to use it so the box sees the TV as always-on/always-connected. Then it shouldn't make any difference if the TV is turned off/on again.
I have no knowledge of these mini Beelink devices, but whereas CEC is native on most ARM SoC boxes (aimed at the Android STB market) most x86_64 devices (aimed at Desktop Windows users) don't natively support CEC control over HDMI.