The universality of quantum theory has been questioned ever since it was proposed. The key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed information-theoretic witnesses of non-classicality with the theory of temporal entanglement. We provide a protocol to witness the non-classicality of a system by probing it with a qubit: we show that, assuming a general conservation law, violating temporal Bell inequalities on the qubit probe when one of the measured observables is the local conserved quantity implies the non-classicality of the system under investigation. We also perform proof-of-principle experimental emulations of the non-classicality witness, using a three qubit Nuclear Magnetic Resonance quantum computer. Our result is robust, as it relies on minimal assumptions, and remarkably it can be applied in diverse contexts, from quantum biology to quantum gravity.