The 'boot time' ( the time to crank up the CPU, load the maps, and have a useable User Interface ) and the GPS chipset Fix time are not directly related, they both start independently at power-up.
They depend on different things.
The CPU boot time will be largely determined by the mapping you have installed.
The GPS Fix time will be a function of how far in distance and time since it last had a fix.
I usually power it up as soon as I arrive at the HQ, and then start the navigation for the first segment before I go inside.
Because on the slow CPU on the device, the route calculation can take a few minutes before it's ready to go.
Likewise, at any control where I switch to a fresh Route, I always Stop navigating, and Start navigating the next segment, as soon as I arrive at the control. I let it do the calculations as I go to the café.