The historicity of Krishna is a genuine question and it has a precise shape. There is strong early evidence for a cult, and no independent evidence for a person.
The cult evidence is good. Panini's grammar refers to Vasudeva and Arjuna as objects of worship. The coinage of the Indo-Greek king Agathocles, around 180 BC, shows Vasudeva-Krishna with conch and discus, and is described as the earliest unambiguous image of the deity. The Heliodorus pillar at Besnagar in Madhya Pradesh, of about 113 BC, records that Heliodorus, son of Dion, a Greek from Taxila and ambassador of King Antialcidas to King Bhagabhadra, set up this Garuda-standard of Vasudeva, the god of gods. A Greek diplomat calling himself a Bhagavata in central India in the second century BC is a very solid datum. What it shows is contested at the edges: Edwin Bryant reads it as conversion, Harry Falk as the ordinary Greek practice of dedicating to local gods.
The person evidence is thinner and disputed. The Chandogya Upanishad at 3.17.6 names a Krishna Devakiputra, Krishna son of Devaki, which is the later Krishna's matronymic. Max Muller and others treated this as a possible source of the figure; the objections are that the verse could be an interpolation and that the name may belong to someone else entirely. W.G. Archer answered that the coincidence of the two names in one verse is not easily dismissed. That argument is live and unresolved.
Beyond that, claims escalate quickly. Guy Beck has written that most scholars accept Krishna's historicity and that he likely lived before 1000 BC, while conceding enormous contradictions in the chronology. That goes well past what the material evidence supports, and it belongs to Beck rather than to the field. The defensible statement is narrower: a Vasudeva-Krishna cult is securely attested by the second century BC, and a historical individual behind it is neither established nor refuted.