Yes, Lt Vance said that Lanza "wasn't let in willingly". He wouldn't say that Lanza shot the window out to get in, but he did admit that the 'swat team' members did break a few windows upon entry.
It seems logical to accept Lanza shot his way in.
But I wonder why Lt. Vance avoided saying Lanza shot out the window.
Possibly because at the time he was not 100% sure. If he wasn’t buzzed in and he didn’t shoot the glass out and get in, then the only other possibility is if as someone was leaving or going in he just grabbed the open door and went in. I’m assuming that they have video but at the time they just may not have examined it and didn’t want to go on the record yet.