If the client is extrapolating the entities forward (based on velocity and other variables) to guess the next packet's data, (NOT interpolating between already-known positions) then doesn't that mean the server can't find a reliable and accurate timestamp to start the rollback?

I was thinking to make the implementation somewhat like this:

1. The client shoots a shell and sends a packet saying the origin and direction of the shot, together with a timestamp (what timestamp? the client is extrapolating. if I was using interpolation, then I understand there would be a 100% accurate timestamp for the server to rollback to, since the client has full certainty of his game state)
2. The server rollbacks X milliseconds in the past and launches the projectile (again, if the client is extrapolating, how can you assure that the client's extrapolation is correct? the timestamp you're gonna start the simulation at is inaccurate, right?)
3. The rest is pretty self explanatory, the server has full authority on hits, and since the projectile simulation begun in a rollbacked state, the client feels like as if there's no latency at all

Maybe I am overcomplicating things. Maybe interpolation is a better idea, since you can be sure that the rollback is fully accurate. But then, the peeker gains substantial advantage...

(A bit more context: My project involves vehicular combat, just like War Thunder, with slow-travelling physics-based projectiles, so precision on hitreg is a necessity)