Step response of high-powered servo motor
The parameters you want to look for are moment of inertia and torque. Looking at the datasheet at the link you provide, page 5, you can find a table: what you are looking for is the second and the third column. The equation of your interest is \$\tau=I\alpha\$, that is the "rotational equivalent" of \$F=ma\$. Solving for \$\alpha\text{: }\alpha=\frac{\tau}{I}\$. Calculating alpha you can have a rough estimate of the time your servo needs to speed up to full rpm. Keep in mind two things:


You will need to add upp the moment of inertia of your sistem
You can probably set up the speed up time in the controller so it might be slower than expected for this reason


For example, looking at the first row:
$$\tau=0.32\ Nm\text{, }I=0.037\ kgcm^2= 3.7\cdot10^{-6}kgm^2\text{, so }\alpha=8.65\cdot10^3\frac{rad}{s^2}$$
If you want to speed up to the rated speed, that is \$\omega=3000\text{rpm}=3000\cdot \frac{2\pi}{60}\frac{rad}{s}=314.2\frac{rad}{s}\$, you can easily compute \$t=\frac\omega\alpha=\frac{314.2\frac{rad}{s}}{8.65\cdot10^3\frac{rad}{s^2}}=36.3ms\$

That's not that much isn't it? Again, I am assuming that the acceleration is costant with speed, which may or may not be true.

I suggest you to calculate the moment of inertia of the system you want to drive and then contact the manufacturer and ask them which servo will allow you to respect the speed up constraint that you have.