it is an ANALOG amplifier, there's really no "threshold" voltage. it will amplify whatever input is there. if the input is below the noise floor however, the actual signal will be difficult to tell from the input stage noise. TL072, (082,etc...) are relatively low noise devices, so a 500uV signal probably will not be a problem to amplify. you didn't mention what the source impedance is, and that makes a big difference in noise levels. avoid large value resistors (if you can), as they generate noise that's proportional to their resistance. use metal film resistors. also make sure your power supply is regulated and well filtered. with signal levels smaller than 1mV, you might want to look up "guarded inputs", which is not exactly the same as shielding, but can be better at reducing noise and such at the input of a high gain stage.
to minimize offset errors, terminate both inputs to ground through equal resistances (actually the noninverting input termination should be the same value as the inverting input termination in parallel with the feedback resistor. this balances the input bias currents and minimizes offset). so if the inverting input is terminated with a 1k resistor and the feedback resistor is 1Meg, the termination of the noninverting input should be 999ohms.