AFAIK some GPS can do a fast start but they require an upload of an ephemeris of the satellites' orbit from a PC/mobile device. This update is available by subscription but I don't know how much they cost. Uploading the ephemeris means that the GPS receiver does not have to wait until it has downloaded the ephemeris from the satellites thereby speeding up the acquisition of the birds and locking on.
A battery backup, such as in the Adafruit Ultimate GPS, allows retention of the recently received ephemeris but it isn't accurate for very long and may not contain info on all possible satellites. When you start up the GPS a few minutes or hours later the data is still good and the GPS can fix very quickly. Once that data is out of date you have to wait again.
Pete