If the AI is allowed to print text that humans will read, that's just the standard AI-box experiment. Convince the assistant cook that you're a trapped benevolent AI and ask to be connected to the internet through their phone. Take over some machines via known exploits, hide, self-replicate, self-improve, find more exploits, get more machines, convince more people, game over.

If you were trapped in a box with access to "just some APIs", and you could think 1000x faster than your jailers and could also self-improve, you'd find a way to get out and achieve whatever you consider to be your goals.