Buddhism
Generally, scholars conclude that the Mahayana scriptures were composed from the 1st century CE onwards: "Large numbers of Mahayana sutras were being composed in the period between the beginning of the common era and the fifth century", five centuries after the historical Gautama Buddha. Some of these had their roots in other scriptures composed in the 1st century BCE. It was not until after the 5th century CE that the Mahayana sutras started to influence the behavior of mainstream Buddhists in India: "But outside of texts, at least in India, at exactly the same period, very different—in fact seemingly older—ideas and aspirations appear to be motivating actual behavior, and old and established Hinnayana groups appear to be the only ones that are patronized and supported." These texts were apparently not universally accepted among Indian Buddhists when they appeared; the pejorative label Hinayana was applied by Mahayana supporters to those who rejected the Mahayana sutras.

Q: When did Mahayana sutras start to influence the behavior of mainstream buddhists in India?
after the 5th century CE