One possible way this could have happened would be if so-called "Greco-Buddhism" had taken hold and flourished:
Greco-Buddhism, sometimes spelled Graeco-Buddhism, refers to the cultural syncretism between Hellenistic culture and Buddhism, which developed between the 4th century BCE and the 5th century CE in the Indian sub-continent, especially in modern Afghanistan, Pakistan and north-western border regions of modern India. It was a cultural consequence of a long chain of interactions begun by Greek forays into India from the time of Alexander the Great, carried further by the establishment of Indo-Greek rule in the area for some centuries, and extended during flourishing of the Hellenized empire of the Kushans. Greco-Buddhism influenced the artistic, and perhaps the spiritual development of Buddhism, particularly Mahayana Buddhism, which represents one of the two main branches of Buddhism.
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I submit to you that if this had happened, Greco-Roman scientific rationalism and science would never have experienced the crushing repression that it was subjected to in the Middle Ages under Christianity. In my personal opinion, the iron-age desert Abrahamic faiths tend to encourage a retrogressive, violent, and atavistic mindset, and one that is not compatible with science and rationalism. There is much more room for empirical thought in Buddhist mental frameworks, and I believe that Buddhism is ultimately more healthy for the human spirit. Without the dark ages stretching from the decline of Rome to the Renaissance, science would have developed much further, while at the same time a Buddhistic outlook could have obviated many of the more warlike events of European history. We'd probably be building our first interstellar star ships right about now, not to mention living in a much less oppressive and environmentally degraded world.