Singular "... a Triac ..." implies it could be a single phase motor. There are several types of single phase induction motors, differentiated by whether the auxiliary/starting winding* is permanently powered, and by whether or not it has a series capacitor to provide the phase shift, with some switching in a starting capacitor in parallel to provide additional auxiliary winding current and thus torque during start and run-up. The remaining type, shaded pole induction motors is very unlikely to be used at this power level due to their low efficiency.
If it has a switched starting winding or start capacitor, using any sort of electronic or time delay switching, that isn't likely to 'play well' with a TRIAC soft start circuit, so you'd need an extra TRIAC to manage the starting winding switching. If it uses centrifugal switching, that should work OK, and your circuit will not need to take over the switching function.
Note that for induction motors with a switched starting winding, (rather than a permanently connected auxiliary winding), it typically has a fairly low duty cycle limit, and can burn out if the motor is restarted too frequently or if the start time is excessively extended, e.g. by shaft load that's marginal for the starting torque of the motor. For those with a switched capacitor, (whether in parallel with the auxiliary winding's run capacitor or on its own simply in series with the starting winding), it is typically a non-polarized electrolytic and also has a low duty cycle limit as its can size is almost invariable insufficient to dissipate the heat from the I2R losses due to the start winding current flowing through its ESR. If you let it absorb too much energy, its electrolyte boils and the capacitor vents, sometimes explosively - game over!
If the motor isn't protected by an overload relay, then your soft start circuit needs to perform that duty as well, which it may need sensors for, e.g. for motor speed, winding currents, and stator winding and/or start capacitor temperature.
* The second winding is generally known as the auxiliary winding if its powered while the motor is running and the starting winding if its only powered during start and run-up. Some reversible motors use identical main and auxiliary windings connected at one end by a run capacitor, and the other commoned together, the direction being determined by which side of the run capacitor you apply power to.