People are specialised for a reason. Flying crew are not engineers and engineers are not flying crew. Each may know something about the other, but ultimately this is largely an engineering issue. Before doing anything, one needs to make an assessment of structural issues (e.g how deep is it in the mud. 2 inches in ice mud or 12 inches ?) . Can one put equivalent of planks under front of wheels to eases path etc. Does one need to offload ?
Sometimes lateral thinking , without knowing the boundaries can be dangerous.
Clinton also got stuck in the mud.