Hire an auger. Six inch for a three inch post. All the way through to sub soil.
You will end up with a big hole if you dig.
Hard way is use a gad-pry - a long fencers bar - to poke and round out a hole, then drive your post with a point on it from above with hand held post knocker.
Be certain with both methods that there are no services.
Disclaimer: Woodenspoons takes no responsibility for explosion, gas leak, sewage outfall disturbance, electricity mains disruption, maiming or death as a result of following his advice.