fft - FMCW Radar Working Logic Question

In FMCW radar rather than sending a signal at a constant frequency we are sending a chirp which goes e.g. from 6 GHz to 6.1 GHz in 5 ms.

What I cannot fit in my mind is this (numbers are just for example):

The RF signal is moving at the speed of light so while we are changing the chirp frequency linearly e.g. we start from 6 GHz and waited like 500 us, then increased it to 6.01 (up to 6.1 GHz) and we already received the 6 GHz signal from receiver without completing 5 ms chirp period. So up to this point we have nothing to do with other frequencies of chirp (6.02, 6.03, ..., 6.1). Basically how IF shift in signal occuring. Is it occuring for every frequency part of the chirp signal (6 GHz for 500 us, 6.01 for 500 us ... up to 6.1 GGz) or is it occuring as a result of whole chirp package?

Shortly should i just simultaneously change chirp from 6 to 6.1 and 6.1 to 6.0 back and forth and at the same time A/D convert the upcoming signal and save it somewhere until it makes 5 ms then plot the fft of the whole 5ms block.

I hope I am clear. Please show me what I am missing here :)

LATER UPDATE: Everyone is trying to make me understand the theoretical background where i already know but thank you guys for your time.

I am teling this with examples so people who have same problem in future can understand. While sending a chirp we start sending with a fix freq. as a start point like 6ghz. While it is traveling to the target and coming back a little bit of time passed and during this time our TX chirp signals freq. changed a little bit linearly like 6+X GHz so multiplexer difference is X Hz. Therefore this change depend on the distance of the target since let say target is so far far away we will maybe receive the first signal which was at 6GHz while our chirp is at its halfway of 6 to 6.1 GHz cycle. So the difference will be like 6.05-6=0.5GHz.

Another way of saying, for stationary object nothing happening on the transmitted signal(doppler effect says reflected data is radited with same structure if object is stationary) but until the transmitted signal come we changed the transmitted signal so the upcoming signal will be multiplexed with different freq. signal and based on this change we are telling this is object at this much distance. Thank you