The turbo is always spinning, as far as how early it starts producing noticeable boost, no idea. The motor feels pretty linear to me so I couldn't wager a guess as to what the boost curve looks like.
The turbo needs enough gas volume/velocity to produce maximum boost, not some electronic activation, so below ~2000 rpm there is little gas volume/velocity and little boost produced. Without a boost gauge you don’t know the amount being produced at any engine rpm/load. I have an OBD tool which shows real-time boost pressure, and total boost depends on rpm, throttle opening and load. I usually see full boost (~10 psi) before 3000 rpm at WOT. .