I'm not an Orthodox so I don't know all the details, but do you mean the war didn't start when the Meccans plotted to murder MP in Mecca and sent men from all the tribes to kill him as he slept but found Ali had taken his place in bed? Or when Abu Suffiyan went to hunt him down and kill him after discovering he had escaped?
There was no war when Muhammad was living in Mecca.
Was Muhammad mocked? Yes.
Was Muhammad persecuted? Yes.
Was there an assassination attempt on Muhammad? According to the Muslim's version, then yes. There are no records of such attempts being made from the other side, so it cannot be confirmed. But I would say it is possible.
Did Muhammad and his followers leave Mecca, because he feared for his life? Again, that is a possible "yes", but it cannot be confirmed.
None of these, even the alleged assassination attempt amounts to a war.
An assassination can start off a war, but by itself, an assassination is not a war.
You clearly don't understand what is a war.
War can only begin, when one side declare war, or when one surprise the other by attacking first. Muhammad attacked first.
The real war didn't begin, until they have already moved to Medina, WHEN Muhammad began the armed conflict, via the raids on merchant caravans, going in and out of Mecca, between 623-624. Neither declared war, until Mecca was provoked by these raids (12 of them according to Muslim sources) and when the first real clash happened at the Battle of Badr in 624.
Do you know what started the war in World War II?
No one declare war. The war started the moment German quickly invaded Poland, in a blitz attack. The Poles were completely taken by surprise. The whole government just simply collapsed.
Like the Nazi Germans, Muhammad started the war by attacking first, those raids were pretext of starting the war.