Mash jump at the start to trigger an OOB trigger that spawns dad (The game will crash unless you walk to the door) Pause the game the exact frame after dad says thanks then unpause on the next frame to trigger dad to turn into Mario early (was originally thought to be TAS only) Finally, mash a & b before Mario starts talking and you'll be able to move during the dialog, then, spindash to the top right corner of the map to skip the short wait after Mario finishes talking.
@ZuperZonicZZZ using turbo mode makes it 16 seconds i don't have that much knowledge about the game so if you know any other tricks then let me know so i can get a better time.