Hello, "Free Mode" on title screen unlocks after passing the intro segment in Story mode (also teaching the gameplay's basics), more specifically after finishing the training with Woman Tamer (Black). There will also be a notification 'Free Mode unlocked'.
In case you'd want to skip this, feel free to check the game's Discord server (on General channel, in pinned messages, you can find a completed game save file).
Cheers,
~NK