I don’t understand how not doing this is even an option, assuming trucks follow classical physics.

Or maybe that is the problem and the sign was too small for “trucks - despite the name, please don’t quantum tunnel through the tunnel”.

@standupmaths imagine a truck with an upper section and lower section, with supports on the front and back holding up the upper section, but otherwise a big ol' empty gap between. The front and back supports are strong enough to hold the entire upper section on their own. As the front of the truck approaches the bridge, the front support detaches and lowers allowing the bridge to go through the truck. Once the front has cleared the bridge, the front support is re-engaged, and the back support detaches allowing the bridge to pass cleanly through. Now the truck can far exceed the bridge height, just has to be longer than the bridge width.
@standupmaths to make it more fun, instead of separate supports, it's just a giant rotating ring with a section cut out of it. I think it would have to be comically tall compared to the bridge height.
@zeda @standupmaths
Or, to simplify matters, the upper section is levitated on superconducting magnets.