I had a similar experience in the early 60s as a teenage schoolboy. I was trying to get home from boarding school to Jersey for a long weekend break and had made it by train to SOU for the evening BEA Dak flight. It had been raining heavily for a few days previously and SOU wasn’t blessed with any tarmac runways in those days.
Taxying out to the threshold we became firmly stuck in the mud. After some serious spade work by the resident BEA staff all the male passengers were invited to deplane, (BEA Daks had airstairs) and push on any available piece of undercarriage leg we could get a grip on. I can only think the engines were turning to help (I doubt there was a tug on the station), but the upshot was we got out of the ruts and after climbing back on board we continued the flight and get back to JER 30 minutes or so late.
H & S would have a heart attack now, not only were we in close proximity to whirling propellors but there wasn’t a high viz jacket in sight!