From cold start. Most starts are not cold. The phone knows where it is, approximately, what time it is (within a second or so, from built-in RTC), and orbital parameters of the satellites overhead (maybe without the latest corrections).
My Garmin watch gets a GPS lock in way less than 5 minutes without any cellular connection.
Actually, your Garmin probably gets A-GPS data uploaded to it via the app.
I think that because Huami/Amazfit/Xiaomi smartwatches already do that. We know this from reverse engineering efforts in Gadgetbridge, but support for Garmin is still new and so there isn't as much info about it; either way it probably works in the same way.
My first GPS Garmin watch used for running back in 2011 didn’t have an app and didn’t have any cellular signal. I put it on my wrist and started running. I don’t remember it taking more than a minute to get a signal.
My Garmin watch gets a GPS lock in way less than 5 minutes without any cellular connection.