predicted scaling from a microscopic system – dominated by quantum fluctuations – to a macroscopic one – characterized by stable phases – and the associated exponents and phase diagram have not been observed so far. In this work we couple a single transmon qubit with a fixed coupling strength g to an in-situ bandwidth κ tuneable superconducting cavity to controllably approach this thermodynamic limit. Even though the system remains microscopic, we observe its behavior to become more and more macroscopic as a function of g/κ. For the highest realized g/κ≈287 the system switches with a characteristic dwell time as high as 6 seconds between a bright coherent state with ≈8×103 intra-cavity photons and the vacuum state with equal probability. This exceeds the microscopic time scales by six orders of magnitude and approaches the near perfect hysteresis expected between two macroscopic attractors in the thermodynamic limit. These findings and interpretation are qualitatively supported by semi-classical theory and large-scale Quantum-Jump Monte Carlo simulations. Besides shedding more light on driven-dissipative physics in the limit of strong light-matter coupling, this system might also find applications in quantum sensing and metrology.