Ezekiel identifies the current time as the fifth year of King Jehoiachin's exile (the next verse, Ezekiel 1.2). Ezekiel proceeds to give dates according to this exile. (Notice Ezekiel's prophecies are not all arranged in chronological order.)
- the sixth year (8.1)
- the seventh year (20.1)
- the ninth year (24.1)
- the tenth year (29.1)
- the eleventh year (26.1; 30.20; 31.1)
- the twelfth year (32.1; 32.17; 33.21)
- the twenty-fifth year (40.1)
- the twenty-seventh year (29.17)
Ezekiel 33.21 tells us that, 'in the twelfth year of our exile', the Jews in Babylon receive a messenger telling them Jerusalem has been destroyed. This event took place c.587-586 BC, which dates the exile (of Jehoiachin and these others Jews in Babylon) to c.598-597 BC. Ezekiel 1 sets us five years into this exile.
It is during this time, c.593-592 BC, that Ezekiel says he is 'in the thirtieth year, in the fourth month, on the fifth day of the month'. Going back thirty years puts us c.623-622. The only event of Israelite interest that could be dated to this time would be the discovery of the covenant scroll in the Jerusalem temple (cf. 2 Kings 22).
Dating the 'thirtieth year' as being Ezekiel's birthdate is an ancient proposition (Daniel Block suggests Origen is the earliest known proponent: Block, The Book of Ezekiel, Chapters 1-24, p.82). But identifying the 'thirtieth year' with Ezekiel's birth is just as speculative as identifying it with the discovery of the law in the temple.
We can say for certain it's not related to the exile that Ezekiel proceeds to date the rest of the book with.