Depending on how many rotations the arm encoder does, the absolute function of the encoder will tell you where it is within one revolution, across reboots. Even if it’s more than one, say you had a 2:1 gearbox, you could know what side of the arm it would start on and guess.
However, assuming its multiple rotations, you can use a limit switch to zero the encoder when the robot is booted. ie run the motor in a known direction until the switch is triggered, then set the encoder to zero. That way you have a reference point at which to reset it.
There was a short discussion here: