Within seconds there is mass chaos with hundreds of kids adults running for their lives as well as classrooms going into lockdown. In this case the pos also set off a fire alarm to add to the chaos. With the limited number of officers that can respond within that 0 - 10 minute window the ability to control that perimeter is challenging to say the least, especially if the shooter can easily mix in and there is a lack of physical descriptors.
However, that's where you rely on the Active Shooter training that teachers and students receive. They help to control that mass panic and confusion while responding officers are inside hunting the pos down and getting information from witnesses they can broadcast out to other officers that are forming that perimeter.
But, if you have no one immediately inside hunting the pos down and relaying information to those establishing a perimeter, and engaging him before he has time to exit or kill even more, that is a big problem.
I get it happens fast and there is confusion in the early stages but if these deputies were in place observing the kids coming out I find it hard to believe the shooter wouldn't be more disheveled, sweaty(Florida) and/or have an imprint of a gasmask on his face(some reports have him wearing a mask or gas mask). It is second guessing and there was the delay of the security feed but I can't believe there wasn't at least one indicator as to the suspect. In the end I can see getting as many students out of there as soon as possible.