I know you think the battle of Dhu Qar did happen in 622 and stand for the beginning of the arab-sassanian war
It is possible that I gave this impression but it is not what I think. I consider Dhu Qar as just an event of this war. Not the beginning.
but, even if that date was right (tradition put it 10 years sooner at best), which battles did happen between 622 and 628, and which sources do back this up ?
None source yes. However, I still do not see why Muslims narrators would have invented it as they pretend that it is the Mecca/ Kaba frame which is the trigger of the conquest. If you have any ideas...
This victory was so important to Arabs that it has to be integrated necessarily one way or another into the Muslim narrative because it was not really possible to not talk about it or to make it forgotten. They cannot escape to it. That is what I think.
Muslims believed that an Arab prophet in Mecca/ Kaba existed who was responsible of the Quranic texts and they knew that Iraqi people were talking of a great battle against the Persians
outside this Mecca/ Kaba frame which was supposed to have been the (only) trigger of the war against them.
As they did not want that this event be outside the Mecca/ Kaba frame and the (formidable, marvellous, great, etc) Prophet not be implied one way or another, they integrated it in the narrative.
In doing so, they could not have suspected that integrating this battle in their narrative will give an indication for those (like me) who will contest the Mecca/ Kaba frame they give (because they believed in it as "historical", since it explains the existence of the Quranic texts) of the conquest.
That is my reflection. As usual, I'm open to any refutation...
About the beginning of the war, reread (carefully, each word counts) the sources.