Clicking sound

This clicking only starts and occurs when starting to drive? Does it sound like it is coming from inside the vehicle, or outside in the engine compartment. There are some concerns with exhaust leaks. Often times there are broken bolts at most typically the #5 cylinder, which is closest to the firewall. There could also be a crack in the exhaust manifold. This can diminish when warm as the metal expands and seals.

There is not much behind the dash that could create a clicking sound, that and I have yet to be faced with a similar concern. Is it a repetitive clicking, and how long does it last? What happens if you have the climate control off. There is the HVAC actuators for the climate system, I am not sure if at key off they go into a home position and then reposition at key up. I have seen some things recently that are affected by the inertia of vehicle movement, in either lift/dive or pitch/roll. Take for instance a blower motor shaft, as the vehicle is thrust forward, this will apply forces to the blower rearward, and possibly cause noise. Since I can't hear it, I can only offer suggestions. I have had the dash out of several H3's, and there is not much back there that could cause a clicking noise, especially on a one time, first launch scenario.

Does it have a navigation radio? How long have you had the vehicle, and has it happened ever since? Could it be considered normal, possibly?

It could be initialization(charging) of the ABS hydraulic system, I would guess.