Krishna is transcendental. He is the Supreme Person who lives eternally in his transcendental abode and he descended five thousand years ago to this world to re-establish cosmic order. The activities he performed during his descent can be called historical, though, accurately speaking, they are eternal, manifesting to human vision through history.
Krishna’s historical evidences has been verified by rigorous research conducted over the last several decades in several independent and concurrent sources. There are many yet Let’s consider three such sources:
Archaeastronomy: The Mahabharata describes many unusual astronomical formations, especially the alignment of the sun, the moon and the six visible planets in one line at the onset of Kali yuga five thousand years ago. Today we have astronomical software that, when fed particular coordinates and dates, displays approximations of the sky as our remote ancestors saw it. Using such software, scientists have found that the Mahabharata’s astronomical formations did indeed occur approximately five thousand years ago, with the unusual planetary alignment taking place in 3102 BC.
Archaeology: Underwater expeditions of the coast of modern day Dwarka discovered the submerged remains of the ancient Dwarka city as described in the Mahabharata and the Srimad Bhagavatam. The recovered artifacts like the seals and coins bearing names and insignias connected with Krishna demonstrate that the scriptural descriptions of Krishna are not mythological but historical.
Literature: Krishna is mentioned not only in the Vedic literature themselves, but also in non-Vedic literature like the Buddhist Sutrapitaka and Lalitavistara. The Vedic literatures may be charged with trying to “build a Krishna myth”, but not these non-Vedic literatures, for they often describe Krishna negatively. But even while trying to discredit Krishna and his teachings, they never deny his historical existence, thus indirectly yet strongly demonstrating his historicity.