The FFT will produce an amplitude and a phase spectrum.
You can estimate the distance by examining the phase.
The relationship between (group) delay and phase is explained in the initial part of my lecture notes attached.
Of course you need to think and understand what you are doing. I suggest setting up an experiment to confirm whatever calculations you do... and remember that 'c' is big, so small errors in the estimation of phase will cause errors on the estimation of the distance.