Actually, I beg to differ, it is entirely possible to grab the time, and in fact has been done so to some extent.
A while ago when the update came with the ability to grab Player ID’s, many users took interest in the subject and explored deeper. What was discovered was that those random integers and letters embedded into the URL link of a Gimkit game was actually a Unix timestamp. This lead to the idea about being able to figure out when someone joins in and there was a short period of discussion on implementing this in idle games, but it never came around.
Here’s a guide on it, although it was only able to get to days, but it is possible to get as exact as the time.
I hope this helps.
(cool thing is this works even when the tab is offline or closed if that’s what you were looking for)