We explore the possibility that quantum physics and time arise both as necessities, to explain situations where the global states of composite systems is incompatible with given marginal states. On the one hand, there are marginal probability distributions that do not admit a classical global probability distribution, and yet could be marginal states arising from a global quantum state. Thus, quantum physics could be seen as arising from the requirement that such marginals can exist. Likewise, there are quantum marginal states which do not admit a global quantum description. However, it turns out that they could be marginal states arising out of states pertaining to many-instant temporal quantum correlations. This would suggest that time itself could be a consequence of the requirement that there are marginal quantum states that are incompatible with a global quantum state. In other words, apparent inconsistencies in classical probabilities require quantum theory to be postulated; while apparent inconsistencies in quantum states require time to be postulated.