ANP no AVA: Clunk when shifting from park to drive – mounts or transmission?

I've noticed on my 2013 BMW 328i that when I shift from park to drive or reverse to drive, there's a noticeable clunk or thud from underneath the car, almost like something is taking up slack. It doesn't happen every time, maybe half the time, and it's more noticeable when the car is cold. No vibration, no harsh shifting once I'm moving, just that initial engagement clunk. A mechanic friend said it could be worn engine or transmission mounts allowing too much movement when the driveline loads up. Another person said it might be the differential bushing or driveshaft center bearing. I've been looking for veteran mount installation specialists that can inspect the mounts and bushings without trying to sell me a transmission rebuild. Has anyone here fixed a clunk on engagement with new mounts? And how can I tell if it's the engine mounts versus the transmission mount? Car has 150k km and I doubt any of the rubber components have been replaced. Thanks for any diagnostic tips.