The idea of measuring distance by the time of signal having known speed probably predates Newton. Atomic clocks - one of the technological enablements to a satellite navigation system - were initially created with masers which Basov and Prokhorov helped to invent.
You already know about the technology to launch those precise clocks to orbit.
Sputnik was the first satellite. Everyone with a smartphone relies on satellites. GPS is a more sophisticated radio beep, but Sputnik is essentially the proof of concept of the idea.
"It was October 4th, 1957. Scientists at MIT noticed that the frequency of the radio signals transmitted by the small Russian satellite increased as it approached and decreased as it moved away. This was caused by the Doppler Effect, the same thing that makes the timbre of a car horn change as the car rushes by.
This gave the scientists a grand idea. Satellites could be tracked from the ground by measuring the frequency of the radio signals they emitted, and conversely, the locations of receivers on the ground could be tracked by their distance from the satellites. That, in a nutshell, is the conceptual foundation of modern GPS."
You already know about the technology to launch those precise clocks to orbit.