Opamps also have an input offset voltage spec. For most cheap opamps like 741 or TL071 it is a max of 6mV. Which means if the sensor gave a zero output voltage and the opamp has a gain of 1000, its output voltage will be anywhere from negaive 6V to positive 6V, each opamp would have a different voltage.
You can null the input offset voltage with a trimpot connected to the opamp, or just purchase a more expensive opamp that is laser-trimmed in the factory for low offset voltage.