Literally the first two google results...
https://robomechjournal.springeropen...oth%20surfaces.
https://www.reddit.com/r/robotics/co...ld_this_be_an/
So it can be done. One uses vibration, the other carefully chosen gear angles and slippy plastics.
But the choice of a DC motor doesn't match the application, nor the high breakaway/low running torque on the output pinion. The running torque should be highly variable when pushing a 1:100 or more gear increase. Particularly with a heavy DC rotor on the worm output. I'd expect to hear or feel the rotor spinning.
I dunno... but if it was me, I'd do a few more experiments.