Interestingly, the cold lock acquisition time is usually gated by the time required to download the almanac from the satellites, rather than acquiring the actual GPS signal. The almanac (which is the stuff that basically tells you where the satellites are, so you can figure out where you are based on that) gets sent on a side channel at a very slow rate, something like 50bps, such that it takes about 30 seconds before you have all the data, and any interruption can mean it takes multiples of that. The main advantage cell phones have is the fact that they can download that data from the cell network rather than waiting for it to dribble in from the satellites directly.

The ability for GPS to (sometimes) work indoors these days is indeed pretty crazy. The signals are already incredibly weak, and you'd think having a roof and walls and pipes and wiring in the way would make it impossible to read them.