My guess is actually opposite of yours though. I think short distance trucking will come last, with long-haul interstate trucking coming first. Short distances don't really need an automated truck... the trucker just gets in, drives, and arrives. Automating/standardizing loading/unloading would be great but automating the driver is less of a win.
On the hand, take interstates. Trucker gets in and drives for upward a few days with multiple mandated stops for naps/food... afaik, it takes 3 days to safely drive from SF to NY because of those stops. Now imagine a self-driving truck where the driver is only responsible for first/last-mile driving and refueling... done in 48 hours flat. 30% shorter transit time, plus whatever fuel/insurance savings the AI driver generates. Not bad.