NodeMCU8266 fails to detect Neo-6M GPS module

[DaveX]

@siddarthNair

It still doesn't enter the while loop

That means that no Software Serial is available on D2:

@siddarthNair

const int RXPin = D2, TXPin = D1;
SoftwareSerial gps_module(RXPin, TXPin);
TinyGPSPlus gps;

Is D2 connected to the TX pin of the Neo-6M module that would emit GPS data? From what you've shown, that might not be true.
Please post pictures and schematics as per:

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Also, since loop() already loops, you could change the 'while' to an 'if'.