Is Time Out before opening tap legal?

Not legal....

But if the game starts with a T, you can grant a TO request after the first shot.

Rules reference is NFHS casebook play 5.12.4SitA.

Here's the rule:
 

5-12-4 ...A time-out shall not be granted until after the ball has become live to start the game. The additional 60-second time-out provided for each extra period(s) shall not be granted until after the ball has become live to start the extra period(s).