Turning off the flames for a moment, just trying to learn and see what could be done better in the future....
The doors I've seen look like very heavy duty old style church or bank doors. If they were chained shut from inside, and had no ready vehicle approach, those doors are not going to be opened easily or quickly without specialized tools. If they could be partly opened before the chains went taut, perhaps bolt cutters could reach in to atack the chains. Do cops carry long handled bolt cutters in their trunks? Maybe they should. I know if every potentially useful tool was in a cop's trunk, they'd be full and weigh a ton. So the cops will need to work closely with the custodians and the paramedics on methods of breeching doors.
The windows on the ground floor appear to me to be the easiest way in. The entry cops need to be quicker to think outside the box ("open the doors no matter how long it takes") and be ready to demolish the windows to get inside. SWAT guys train for this all the time, they even have a term "break and rake," meaning using a two man team with a sledge hammer and a long breaking bar to bust out the windows and clear an opening for the entry teams to go in. If the first floor windows are up off the ground a bit you need to drive a vehicle right up under and stand on the roof, use ladders, or even "boost" one another on shoulders etc. The main point is, windows can be used for a fast entry, with minimum tools, but the mindset must already be there to destroy the windows and go in.
All that said, no cops outside of a locked building can get inside in the few minutes a massacre can occur. Only armed students or profs can stop a shooter in that time frame. Even a cautious school could vet certain qualified profs to keep weapons in pistol vaults with electronic keypads. Even a few profs on a floor with fast access to a pistol could give a margin of safety that cops on the outside can never provide.