[I understand] - GPS Modules - Acquisition speed and accuracy optimisation

Acquisition speed mostly depends on the chipset used in the device, the antenna size and the surroundings (open space vs. inside a building). In any case, a cold start of several minutes sounds like a lot. Modern devices are able to start in less than a minute: GPS Chipset - OpenStreetMap Wiki

What do you intend to use the GPS for? Photo geotagging?