How to prevent servo startup jitter
When powering on an Arduino obviously you won't have the Servo positions (as you say), so you need to determining the position of the servo after turn-on. This is not easy. It would involve additional rotational position sensors.

If you really need the Arduino to power up from being completely powered off then I would "park" the servos to a certain position before power-off. Then during initialisation after power-on return the servos to the parked position, and so clearly they would not move.

Alternatively, you could consider a sleep mode for your robot where the Arduino does not truly power off and therefore the variables containing the servo positions are not cleared.