Single stage High gain amplifier

its a extreme situation with too much ideal conditions to give a trustworth result. for example ur input impedance is too low to detect something so low in volt. for one uV a few miliohms will provide tremendous attenuation and sadly all devices require some currents beign induced during dynamic signal changes even in ultra low cap Jfet transistors just to polarize its gate a shifting currents are required. And bjt have rather too low impedance more they require require tens of microamps to repolarize BE junction or just to maintain such driving voltage and when u will need to do it a few tens of nasty ohms will make ur 1uV hard task to induce such currents now also a noise barrier will be game over for such signal. and used devices and topology also will amplify rather background noise and place another bunch of noises from themselfs in amplification proces.

But speaking theoretically. Let's say i get the input impedance right and filter out all the noises is it really possible for a single stage to have such high gain? I know this much gain is bound to induce noise but for the sake of argument is it plausible?