@insto That's pretty much right.
There's a lot got to happen before you get a 'lock'.
Before it can do that it also needs to get the date/time confirmed by multiple sats.
Once it knows the time, it can work out if it knows the sat position data. If the device has been off for a while it needs new position info for each sat it is talking to which can take a couple of minutes - this is the main delay.
If the initial comms gets interrupted, for example because you started travelling and a building got in the way, it's got to start the conversation over.
I switch my Garmin 500 on as I walk to my bike, and it's usually got a lock by the time I stop faffing and start riding about 3 mins later.
GPS signal is very weak. Regarding the missing airliner in the news, I find it frustrating that the press keep suggesting that the 'black boxes' should be able to get their position from GPS and transmit it. That's not going to work under 1 meter of water, never mind 1000 meters.