If you start with cold water the increasing vapor pressure on the way to boiling will force some of the water through the coffee at varying temperatures, but past that it will reach steady state and end up pushing boiling water. Not sure how much of a difference there is in getting to that point. I don't think pressure matters much since the Bialetti is not a high pressure vessel (maybe 1.5atm probably less if beans are really coarse).

Boiling less quickly (i.e. using lower heat) might put the coffee in contact with boiling water for longer. So it would seem high heat and cold water would be the way to go if you want to minimize the temperature-time product of the beans-to-water contact.