It could definitely be the motor or transmission mount. If you had access to the same make/model and could do a side by side comparison of the experiment above, if the motor mount was the problem you’d probably be able to notice the difference in the amount of engine twisting motion. But without something to compare against, and no experience doing this, you might not be able to tell yourself. Mechanics will often put the truck on a lift and use pry bars to see how much the mounts yield to their prying force, that’s another way to test them. If you shop did that, and they have plenty of experience, if they tell you the mount is the problem it probably is.
fyi Other things can cause clunks when taking off from a start. One very common reason is a drive shaft u-joint has failed. Or if your drive shaft is a two-part version with splines, if the splines aren’t properly lubed it can make a clunk when starting and often when stopping (in gear). Testing for failed u-joints is pretty easy, and lubing the splines is easy to do also. So you might ask your shop to try that first.