Free Roam mode is normally unlocked by completing the game, just before the end credits have rolled. You should have received a trophy called "Firewatch" the first time the credits were triggered, which you could find in the Trophies app on your PS4 System Software.
During the end credits, you should see the in-game photographs you took scrolling by; make sure you have taken at least a few photographs using the in-game camera to verify the "End Game Save" has been written. If you have seen your photographs during the end credits and received the trophy, a file named "End Game Save" should now appear under "Firewatch" in Settings > Application Saved Data Management for your Saved Data in System Storage. If this file exists, you should now see the Free Roam mode available on the Special Features screen accessible from the Main Menu.
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