Is there a best time to play Tablet of Time's Dawn?
No, there is no best time to use that ability to increase your odds of of winning. The thing to remember with cards like this is that a lot of it will depend on how the overall game is progressing. This includes the skill level of your opponents and what mix of cards are coming out

Early/Mid game I find it best used when there is one or more cards in the center that you want to get or prevent others from getting. This works great when paired with cards that have abilities to acquire one or more cards from the center/deck. Even better if you can stack your deck or otherwise ensure you will have those abilities.

End game it is similar but also ensuring that you will be able to get at least get the two honor back that you would lose from banishing it.

Last thing to remember is that even with a deck that can regularly pull out some very good turns it is possible for the extra turn to be a dud. It has happened to me where I end up drawing my entire deck (plus all the cards I acquired that turn) and end up with crap for the following turn.