The big question is why China would send a balloon. My best guess is it carried electronic warfare sensors to try and collect specific information about US radar and missile capabilities. They may have in fact wanted us to shoot it down, ideally first painting it with advanced radar (both air and ground based) and then firing an advanced missile at it. Data could be streamed out until the moment of impact and used to create better ways to jam or avoid US missiles. Sending it over sensitive sites may have been an attempt to force the US to take such action.
I’ve heard rumors that it was shot down by an AIM 9X, which is IR guided, a good choice as its seeker doesn’t use radar and thereby expose the terminal radar guidance information. I’m going to go way out on a limb here and theorize the delay was due to brand new upgrades required to the AIM 9X software to be able to lock on to and hit a balloon, which they probably were not originally capable of.