The GPS signal in below thermal noise at ambient temperature [1]. Using your logic you would say that then it would be impossible to extract. However, with clever math you can extract a signal which is below the noise floor.

Particle physicists are experts at this, extracting tiny signals from huge piles of noisy data.

[1] https://sdrgps.blogspot.co.uk/2016/02/find-signal-in-noise.h...