You could do something simple like:
s = exp(-a*(t-t0)).*sin(2*pi*(t-t0)/T);
and tweak t0 to be whatever time you need the waveform to start at.
If instead your question is more like "I have a uniformly-sampled signal. What are some reasonable techniques to delay the signal by an arbitrary time?". There are a few ways to do that (interpolation, model/curve-fitting, time-shift filtering, fft-based methods, etc.), but they of course are less ideal than having a closed-form expression like the one you have above.
