S-Parameters

You can describe system behaviour in time domain. TDR is measuring a time domain equivalent of S11. Modern VNA calculate simulated TDR response by inverse FFT. Many EM solvers are are working in time domain and calculating the frequency domain result by FFT.

On a more theoretical note, S Parameters are defined as steady-state quantities. If we consider S11 for example, we're looking at the ratio of the magnitude of the received sinusoid to the input sinusoid.

In the time domain, this doesn't really make sense, because we would need more information. If we replaced sinusoid magnitude with instantaneous voltage, we'd be looking at the received voltage versus the input voltage. However, in order for some voltage pulse to interact with your network, you'd have to specify these quantities at different times. What times? Who knows, it hasn't been defined.

What is done in the time domain is just observation of total voltage versus time. You can transform this into the frequency domain, and with knowledge of the terminating impedance, get current and voltage versus frequency, from which S parameters can be computed.