I don't now live in Texas but am a self proclaimed Texan who once lived a hundred miles or so from Uvalde, and with deep ties that go back to the beginning of the Republic ...
Also, I'm an analyst by occupational history, a systems person, and one who has a bit of insight into how government and agencies work, and also have a bit of insight of how the media responds to such incidents.
The investigation is still in process and there are still many unknowns. But, from what I saw from today's press briefing ...
It's uncertain why Salvador Ramos picked that particular door to gain entrance, possibly it was random and just happened to be the closest door when he wrecked his vehicle. Or maybe he intentionally wrecked his vehicle near a door that he intended to use.
They said the door was unlocked and there was no security officer to confront him. Considering the proximity to the (staff?) parking lot, that may explain why that door may have been unlocked, or possibly jimmy-rigged to remain unlocked. Or maybe it was locked and he had the key (I believe his grandma once worked there). Or maybe it was locked and he shot out the locks.
We'll probably learn more about the above later, but regardless of which, per press briefing, he immediately went to one or two rooms and started murdering. By this time the local police were responding and had multiple missions. One was to help lock down the remainder of the school and the other being to find, isolate and engage the active shooter. They did both. Per the press briefing, the local police did all that and was communicating with the shooter who had barricaded himself, and during the engagement some of the police may have been injured. Once cornered and isolated he was possibly no longer an imminent danger except to anyone who tried to charge his position. To take him out completely, without further endangering the police or remaining children required a tactical team with resources, so the role of the local police would have been to keep him pinned and talking until the tactical unit arrived.
The sad part is that the teachers and children were likely all murdered within those first few minutes; but for those next 40 or 50 minutes the local police successfully prevented him from shooting more children. We will at some point know about the communication between Ramos and the police. The significance of that 50 minutes probably affected the lives of those injured who may have been saved had they been given medical attention earlier. Had the local police not waited for the tactical team, their efforts may have instead flushed him out where he could have continued to shoot more children.
This is just my analysis based on the news briefings.
Stories about parents trying to gain access to the building while the shooting was in process are both understood and disturbing because they consumed police resources that may have been better used to lock down and isolate the other children in the building. We don't know whether that shooting was between the local police and Ramos or directed at the children, but considering that the local police were in the building and engaging Ramos, it's more likely that it was between the police and Ramos.