Your assumption may well be right. Quite possibly the MEMS is biased to 1/2Vdd +/-20%. But the datasheet does not give any guarantees. However a couple of 0603 NP0 capacitors for decoupling and DC rejection and two 0402 resistors are not going to increase your footprint that much.
EDIT1: Also the DC output may depend on your local air-pressure, and as such elevation. It may not be a strong response, or even a linear one, but compared to signal levels one or two mV of drift caused by weather effects could already confuse your measurements if you don't decouple
However, what the datasheet does give, is the following:
Sensitivity = -42dBV/Pa
This comes down to about 8mV/Pa output signal.
In this 1 Pa is about 94dB(SPR). So that's already pretty much talking quite audibly into the microphone and you will only get 8mV of signal. I'm not assuming your uC ADC is measuring over a +/- 10mV range, so I don't even think you are going to get away with no Op-Amp.
That said, again an op-amp comes in SOT23-5 case from most any vendor these days, not to mention some more specialty companies may make them in those smaller SOT323 boxes. Even the SOT23 is hardly going to increase your footprint coming from the microphone, let alone a micro controller.
With small footprint for this set-up it comes down more to good placement and good sourcing rather than shaving of components you can't miss.
It seems that microphones were damaged during PCB cleaning process. The producer puts spray on the PCB after production and small particules may enter inside the sound inlet during the process. When we changed the microphones, they started working. This explains the problem.
Best Answer
Some IC's can only handle X °C for Y seconds. It may be possible that you've burned the IC's. You did use hot-air, who knows how hot it actually is right at the nozzle? And take a couple °C off that, that's how warm your IC got. Maybe a few hundred °C. Only you can tell, you got the instrument and you know what you did.
Or, I believe this is your datasheet, if you look at page 11 you'll see that it says "Do not pull air out of or blow air into the microphone port.". It's a very possible thing that you've done, add "very hot" to that problem and you've got yourself something that's probably broken.
If you keep reading on the same page, under "BOARD WASH it says the following:"When washing the PCB, ensure that water does not make contact with the microphone port. Do not use blow-off procedures or ultrasonic leaning.".
So it appears that your microphone is very sensitive, and can probably break if you just blow into the microphone port with your own breath.
Or something is actually wrong with the schematic.
Or something is wrong with some other component inside your circuit.
If you want to be very certain that the problem is not because of your hot-air soldering, then make a sixth and solder it with a regular hot iron.