As I have shown in other posts, a Schmitt has no stable state and must oscillate. The trick is to channel the energy through the crystal instead of around it, as in a plain RC oscillator.
Time domain oscillators start on numerical instability. There are numerous examples in Oscillators.zip where the oscillation starts at zero amplitude and builds up to strength.
It is extremely difficult to couple a pertubation into the oscillator tank to kick start an oscillator. The tank simply ignores the energy in an external pulse. You have to somehow inject the pulse in series with the tank but I have not found a practical way to do that. A simpler method may be to simply increase the loop gain by increasing the drive level.