No, because Blizzard never tells us.
It varies, because it’s not a live, production server. For example…
The announcement for the 2.6.9 PTR being available was posted at 13:50 Pacific.
The announcement for the 2.6.8 PTR being available was posted at 11:17 Pacific.
The announcement for the 2.6.7 PTR being available was posted at 18:01 Pacific.