Probably due to the ATF leaking back down through the anti-drainback valve (check valve) in the coolant line which allows the ATF that is supposed to remain inside the torque converter to instead drain out. The transmission won't move until it has had a chance to refill the torque converter. Your transmission doesn't pump ATF in Park, try letting it sit for a few seconds in Neutral so the pump will work to refill the torque converter.
You can either replace the coolant hard line where the anti-drainback valve is, or splice in a new aftermarket antidrainback valve. FYI in case you go with an aftermarket anti-drainback valve, aka check valve, the hose diameter is 3/8".