Is it possible to play Path of Exile entirely solo?
The closest thing you can get is Solo Self-Found mode. In this mode you cannot trade or create parties. However, you will still see other SSF players in towns - that's the way game developers earn money - they sell fancy microtransaction items for players to show off.
You can try playing less popular leagues / platforms. I think Normal (non seasonal) Hardcore SSF on consoles will have the smallest number of players.