Why Is the Age of Islam Based on the Beginning of Hijrah?
Question

I have noticed when a non-Muslim asks about the age Islam after prophethood we as Muslims answer only with the years after Hijrah. My question is; why do we always leave out the first 13 years of prophethood before Hijrah?
I know the year of Hijrah was a great year yet we all know that prophethood started 13 years before this so when answering why don't we mention this like now we are 1433 AH yet when answering why don't we say Islam after prophethood is 1446 adding the 13 years before the period. insha allah you can explain why we don't add the first 13 years into our answer.
Praise be to Allah.The Makkan period is part of the history of Islam
No doubt the years that the Prophet (blessings and peace of Allah be upon him) spent in Makkah before the Hijrah (migration to Madinah) , when he was calling people to the path of his Lord, enduring persecution and patiently putting up with the annoyance and accusations of the foolish, could be considered as part of the age of Islam; indeed they are among the greatest years of Islam because during this time the Prophet (blessings and peace of Allah be upon him) was relying completely upon his Lord, thinking positively of Him, and patiently bearing persecution for His sake. 
This is something that no wise person would doubt and no one would deny it at all, whether he is Muslim or otherwise. 
Why was the year of Hijrah the starting point for Islamic calendar?
However, the reason why the people adopted the Hijri calendar as a means of defining the year in which a particular event took place, which is something that people need to do, is that this date is the one that the Companions (may Allah be pleased with them) unanimously agreed to take as the beginning of their calendar.
This decision was made at the time of `Umar ibn Al-Khattab (may Allah be pleased with him), because it is the actual date of the founding of the Islamic state, when the Prophet (blessings and peace of Allah be upon him) and migrated and settled in Madinah, and the people gathered around him and supported him, and he built the mosque, and other events that followed the Hijrah.
So the features of the Islamic state began to develop and it took on a clear form geographically, socially, militarily and politically. Before that the Muslims did not have a state or any political system to unite them. 
The Companions (may Allah be pleased with them) reached a unanimous decision in 16 AH – or, it was said, 17 AH or 18 AH – during `Umar’s caliphate, to make the Islamic calendar begin with the year in which the Hijrah occurred. That was because a case was referred to Amir Al-Mu’minin `Umar (may Allah be pleased with him) concerning a contract that one man had with another, saying that what he owed him became due in Sha`ban. 
`Umar (may Allah be pleased with him) said; Which Sha`ban? The Sha`ban of this year we are in now or of last year or of next year? Then he summoned the Companions and consulted them about adopting a calendar from which they could determine when debts became due and the like. 
Someone suggested adopting the Persian calendar, but he did not like that. Someone else suggested adopting the Byzantine calendar, but he did not like that. Others suggested dating it from the birth of the Messenger of Allah (blessings and peace of Allah be upon him), or from the beginning of his mission, or from his migration (Hijrah) or from his death. 
`Umar (may Allah be pleased with him) was inclined to choose the date of the Hijrah because it is known when it occurred, and they agreed with him. 
The point is that they made the beginning of the Islamic calendar the year of the Hijrah, and they made the first month of the Islamic year Muharram, as was narrated from them. This is the view of the majority of Imams, so that people could conduct their business on that basis, with no confusion. (See: Al-Bidayah wan-Nihayah, 3/251-253)
Al-Bukhari (may Allah have mercy on him) narrated (3934) that Sahl ibn Sa`d (may Allah be pleased with him) said: They did not start the calendar from the beginning of the Prophet`s mission or from his death; they only started it from the time of his arrival in Madinah. 
Ibn Hajar (may Allah have mercy on him) said: 
“The incidents that are connected to the life of the Prophet (blessings and peace of Allah be upon him) and that could have been taken as the start of the calendar are four: his birth, the start of his mission, his migration (Hijrah) and his death. They thought it was best to start the calendar from the Hijrah, because in the case of his birth and the start of his mission, there would be uncertainty with regard to the exact year. 
As for the time of his death, they chose not to use it because remembering it would renew their grief. So there was no choice left except the Hijrah. And they chose to regard Muharram as the first month of the year rather than Rabi` Al-Awwal because the plan to migrate started to take shape in Muharram. The oath of allegiance (bay`ah) – that was the precursor to the Hijrah – had taken place during Dhu`l-Hijjah, and the first new moon after the oath of allegiance and the decision to migrate was that of Muharram. So it was appropriate to make it the first month of the year. This is the best explanation I have come across as to why the year starts with Muharram. 
Al-Hakim (may Allah have mercy on him) narrated that Sa`id ibn Al-Musayyab (may Allah have mercy on him) said: `Umar assembled the people and asked them what the first day of the calendar should be. `Ali said: (It should start) from the day when the Messenger of Allah (blessings and peace of Allah be upon him) migrated and left the land of shirk. So `Umar did that.
The one who says that the age of Islam started with the Hijrah is referring to the calendar and the people agreed upon creating a system so that people could know the dates of events and define the times of contracts, the dates of visits by delegations, and the like. This is something on which the people agreed during the caliphate of `Umar (may Allah be pleased with him) and it has remained so up until the present day. The start of this calendar marks, as `Umar intended, the establishment of the (Islamic) state, which only began with the Hijrah.
As for the beginning of Islam itself and people's awareness of it, we do not need to point out that this took place before that time. Indeed the meaning of the word Islam in general includes the religion that Allah approved for His slaves and with which He sent His Prophets and Messengers . But this is not what we are discussing here. 
We do not believe that anyone could imagine that Islam only began with the Hijrah and ignore the years of Da`wah during which the Prophet (blessings and peace of Allah be upon him) and those who were with him in Makkah strove to establish the faith. No one would say this. 
And Allah knows best.