Don't acknowledge the truck until the push is done.
Don't acknowledge the truck until the UNLOAD is done.
If the Super Sorting is done correctly, finding freight on vehicles should be fairly easy (sure, repacks are still troublesome, but the sort should separate them by their fillgroups and you should still be able to find that random Pharmacy item or Seasonal item without opening EVERY REPACK from the unload. Scheduling should have prioritizes those areas to be pushed early these days anyway.
Acknowledging the truck prior to unload is where the real pain happens. Orders will drop for items in the unload, and those items might not come off the trailer until hours after the unload process has started. That's a real issue if you're trying to complete OPUs before the store opens.