The breadcrumbs:
1. When Tony and Dr Strange are leaving the NY Sanctuary Tony says "Can't you put that in your back pocket or something?" Dr. Strange replies "Or I'm gonna use it." When they emerge Dr. Strange has magical bracelets on him as if he had just finished doing something. They never mention what happened at that moment and Dr. Strange never uses the stone during the conflict.
2. Later on Dr. Strange confirms that he has at least one scenario (out of 14 million) that where they win.
3. Dr. Strange bargains for Tony's life suggesting that Tony Stark is part of whatever plan he saw. - or he just wanted to guarantee that someone would survive who knew the plan.
4. Thanos scolds Dr. Strange at the end of the battle on Titan saying that he never used his most powerful weapon. Dr. Strange does not say anything.
5. As Thanos leaves Titan Dr. Strange mentions "now we're in the end game" suggesting that the plan is still in motion.
6. At the end of the final battle Thanos tells Thor: You should have gone for the head.
7. Weird interlude where Thanos talks to child Gamorah.
8. Dr. Strange comments as he fades to dust "There was no other way."

She theorizes that Dr Strange set something in motion with #1 (a marker? loop?) that will allow a replay of the events that occur after he uses the time stone. If you remove all the cut scenes and dramatic pauses there is actually very little time between the moment he uses the time stone to get the mind stone and when he snaps his fingers.

There are two options. Doctor Strange did not use the time stone because:
Dr. Strange has set a loop or "replay" that will allow for Thor to get Thanos in the head the next time it loops around. (Think of the battle with Doromamu)
Thanos has won but it is in an alternate timeline created by Dr Strange and Thanos doesn't know that yet.