Is you hiss as loud as speech at 1 meter? That would equal about 60 to 70 dB. If so, then something is not right. The hiss should be atleast 20dB lower. Or 1/10th of a speech signal at 1 meter.
Next. See what the analog output is of the electret module at your intended SPL. See if you have high enough sensitivity.
IIRC that electret module has a sensitivity adjustment pot.
It might be that you are...
Find out if your ADC reads zero-ish with a low values potenter. And find out what the high values at 3.3v too. Might be better to use an lower ADC reference value to ensure that the electret module can drive the ADC...
The ADC has an effective dynamic range of 13 to 14 bits. That depends on how low you can get the source impedance driving the ADC. So expect at least 4 to 5 bits of random fluctuations rms That’s about 32 LSB rms or...
ADAfruit isn't selling garbage. The MAX4466 will get you to 30dBA if used correctly. Long wires dont cause hiss. An opamp with enourmoud bias current like the costly AD797 is a bad choise for a high impedance source...
The MAX4466 should be able to getdown to 30dBA.. that pretty silent and very suitable to pickup voices from 1 mtr distance, prolly not good enough for distant bird sounds. If you cannt get descent sound from a MAX4466...
These number really depend on you microphone. It normal for a electret mic element to have a building impedance converter that has around 50 to 100 nv/sqrtHz noise. BJT input opamps such as the AD797 are suitable for...
Maybe the microphone isn't able to drive to ADC to its full range?
Or maybe the ADC input isn't biased halfway its range (3.3V / 2 - 1.65 volt)?
Use the 16 bit ADC bit depth to ensure you dont lose resolution.
Then you shouldn’t call it noise.
It is important to keep the impedance to the ADC input as low as possible, so removing that 10k//1n might help. Does it happen when you short the input jack to ground?
And if you...
A single coil has about 6nV/sqrtHz noise, a hum bucket about 10nV. That op amp has 18nV noise and that 10k resistor 13nV. And than the ADC... assuming about 10 LSB rms over 20kHz BW and 3.3volt range. ... that...