Child of God, you asked this same question on the Biblical Hermeneutics site just a few days ago. The evidence I gave there concerning what year was considered the beginning of Tiberius' reign is solid.
For the sake of those not on that site, here is the evidence I offered:
Augustus died in AD14. Thus Tiberius began his reign as sole Emperor. The 15th year, then, would have been sometime during the Gregorian calendar years of AD29-30. This is the time most historians ascribe to the beginning of Jesus' ministry.
Luke took the historian mantle on when writing his gospel. I would suggest he was careful to count from AD 14 because that is when the reign of Tiberius began. Elsewise he might have said the reign of Tiberius and Augustus.
The Roman Senate named Tiberius Emperor Sept 18, AD14. Before that did he serve a leadership role as Augustus' health was failing? Yes. But His reign did not officially begin until AD14. This is considered the agreed upon beginning of his reign for the last 2002.5 years. Luke would have had no reason to consider the "co-regency" as part of Tiberius' reign because no one else did either. The "15th year" is counted from AD14.
Augustus died August 19, AD14 In Annals, Book 1, Tacitus reports that, after the death of Augustus, a Roman centurion attempts to report to Tiberius (7) who replies "I have not yet been given command [of the Roman army]." In Book 1.10, Tacitus writes that Augustus had not chosen and seeming did not want Tiberius to be his successor. If Augustus didn't consider them to be ruling together, I don't know why anyone else would.
Book 1.12 shows that they are trying to name Tiberius as Caesar but he only wants to have partial power. In 13, we read that Senator Haterius says "How long, Cæsar, will you suffer the State to be without a head?" Even though they saw Tiberius as the presumptive Caesar, he was not officially so. The Roman senate recognized Sept 18, AD14 as the beginning of Tiberius' reign.
Not Augustus nor the senate nor even Tiberius himself considered Tiberius to ever be co-regent. Sept 18, AD14 is the correct date from which to measure the 15 years mentioned in Luke 3:1