Having the same issue as of late with my 4K Apple TV—actually for the past two months. I feel like it started happening with IOS 15 and as Apple continued to update versions of IOS 15, it's been getting worse. Currently running the latest IOS in case you're wondering.
The problem is that it's intermittent. Thinking it was a bad HDMI cable, I replaced both cables—from my Onkyo AV receiver to the 4K Apple TV box and HDMI cable from the receiver to my LG TV. Even with fresh HDMI cables, I'm still experiencing a no audio issue upon startup with all apps.
The audio eventually comes on—typically after :60 sec to 2 minutes, it is in sync with the picture and is stable for the remainder of the viewing experience until it's turned off.
Any suggestions would be greatly appreciated.
FWIW, I don't have this issue with my Apple TV 4th Generation which is running the latest IOS.