The boost phase to the release of the Reentry Vehicles, RVs, is a relatively short time and ends in ten minutes or less.
The flight profile of an ICBM last around 30 minutes so the entire powered and steered phase is one third (or less) of the flight and it is all contained within the ascent phase of the flight profile.
Destroying an ICBM containing MIRVs is basically impossible with our current technology. We have to focus on exo-atmospheric and endo-atmospheric intercepts, which means we must have many more missiles to deal with the individual RVs.
I guarantee people have been working for many years on figuring out how to stop ICBMs during boost phase but we are not yet there.
Perhaps the lasers will finally do that. They have been mounted on smaller and smaller test platforms.
Thank You