in any setup with a Sonos Home Theater product (Beam, Arc, Playbase, Playbar) the center of control is the TV. it is responsible for negotiating with and making sure the Audio and Video input streams make it to the right output.
in your situation, the LG 65SK8000PUA needs to be able to be in control and make it all work. the Sonos Arc is just connected to the ARC port for audio sent from the TV for the A/V source you select or apps you run on the TV itself.
if the problem begins when the TV is turned off and then back on but works ok when you connect devices to it after it has been on, my best guess is the HDMI initialization is not working correctly on the TV during power up.
since the power up sequence is where the problems begin i would try the same connection troubleshooting sequence: connect one device when the TV is off, turn it on and see if it causes the problem. then switch to the other device.
another thing to check is the firmware - make sure it’s up to date.
that TV doesn’t appear to have a lot of configuration options for HDMI but you could also try the same troubleshooting sequence above with the Settings>General>SIMPLINK (HDMI-CEC) setting on and then off to see if that changes any of the results.
another power startup related setting is the Settings>General>Quick Start+ option - try it on and off.
