The easier access to and from the shrine is via top of the hill. First picture leaving the cave, second and third pictures taken from top of the hill.
The top of the hill is easier to traverse and high elevation and more sparse vegetation (big pine trees) helps avoiding mosquitoes. Also has room for setting up a tent if needed.
From top of the hill there is two possible directions to exit. To southwest, the official route. Longer route but in better condition. Or to east (unofficial) (shorted but potentially muddy). Likewise places to park a car exist on Pirunlinnantie and Hirvenkuruntie (respectively).
Don't litter. The hill is a historic site and ruins of a castle from 400-800 AD.
Note: there may be a geocache somewhere in that cave. I'm not a geocacher so I didn't bother to search for the box.