Can a VFD reduces motor starting kick?

At zero speed the motor requires torque which is flux (voltage) and current (mostly reactive). Only a little bit of active current to compensate for the motor power losses.
Only the power losses need to be drawn from the grid at that time, which means a very small amount of current. It may produce 200% current on the motor and pull only 10% current from the grid.

Of course, as the motor is accelerating, the motor will require kW and the current pulled from the grid will increase accordingly, as the active power consumed by the motor is increasing.

Regarding the kick of torque on the motor, it is controlled by the maximum current ramp limit or through the speed reference as the ramp rate defines the current and the derivative of that rate is the current rate. For this reason, many large machines will be started using an S-Curve speed reference where the S part will adjust the torque (current) rate to avoid stressing the mechanical components, especially if there is mechanical backlash in the gears.

Actually the starting method depends on the type of motor itself SR or SQ type the voltage supply, the motor capacity and motor function, for the MV Motor a liquid or oil starter was the best solution used before.

In case the operation process required a change in the equipment speed the variable frequency drive (Air or water-cooling) based on the drive capacity is the optimum and reliable solution.

Definitely it reduces starting kick of the motor. Actually, the degree of starting kick of a motor is depending upon the starting speed of the motor. If you start your motor at low speed you will have a low starting kick but if started at high speed, you will have high starting kick. This is generally the condition for low and high kw motors. One factors of varying the speed of motors is by varying the frequency of the motors (from the formula N=120f/p) and VFD drive is use to vary the frequency, thus varying the speed of the motors. But if used for starting only, this is expensive as there is more cheaper way like using the Soft Starter or use a WRIM/Slip-ring motors with LRH/Resistor Starters or other. Normally, variable frequency drive is use on operation with speed reduction/varying requirements at required number of time or continuously.