[Nevadaref]

Originally Posted by BillyMac

Agree that substitutes can come in at these times, but since it's the start of the game, nobody has to sit a tick because nobody came out of the game, and tried to renter.

3-3-4: A player who has been replaced, or directed to leave the game shall
not re-enter before the next opportunity to substitute after the clock has been
started properly following his/her replacement.

If your technical foul after the toss situation happened during the jump ball to start an overtime period (as mentioned by Altor), then the "sit a tick" rule may apply.

Or does, the free throws awarded because of a technical foul may be attempted by any player of the offended team, including an eligible substitute trump the "sit a tick" rule for such an overtime jump ball technical free throw?

The sit a tick rule applies. The team member who exited the game at the end of regulation is simply not an eligible substitute at this time.