I know I could not.. Have to be taller and stronger ... but I see it done with a post hole digger and it does not look impossible. Goes fast too. And, we have clay. Then the cardboard footing tube goes in the hole, wood posts in that and quick set cement and 10 minutes later..it is hardened.
But I would not do that...I would dig the hole...fill it as above with the tube and cement and screw /bolt a treated wood square into the cement. Attach a matching treated wood square to the bottom of the posts and set that on the cement grounded wood. This way could MOVE it when I want to repair, replace, and take it down for storms. This would only work for small doorway arbor entrances... Not a big installation that is part of the house architecture. Saw it recommended once for smaller structures. Also allows it to be built on ground rather than using ladders.