The history of the Bach family of musicians started in the year 1504. That is official and you can check this in a record on your own. Just click here. It is the so called "Church Penance", which is a letter. When exactly this story of the Bachs started and who was born in the year 1504 and most important, where that happened, that is not mentioned in the letter of a Bach to his church. It is exciting, that this letter was written eight years before Johann Sebastian Bach 1735 created his "Ursprung der musicalisch-Bachischen Familie", which is the "Origin of the Bach Family of Musicians".
The year 1619 is the year, that matches better to the whole history of the family of musicians. Because there is a name for the first time, a church document and a musical instrument. Veit Bach has died in that year 1619. In Wechmar, Thuringia. Plus, it's mentioned by Johann Sebastian Bach in person, which counts as a authentic proof. Still today there is the mill located in Wechmar, on the creek Apfelstaedt, it's called the Veit Bach Mill, in which Veit once grinded his grain. Plus, he played on his cittern, which in German and as a historic term back then was a "Cythringen", matching the beat of the water wheel of the mill. It is handed down, that Veit has had much fun making this music.
If you want to be on safe ground regarding the beginning of the history of this family of musicians, best is you consider the first reference back in 1504, when the Bachs were just a family, not yet a family of musicians. From around 1600 the Bach Family became the Bach Family of Musicians and the year 1619 is the first time, a church record mentioned a member of this Bach Family of Musicians. However, keep in mind: this genealogical era is really tricky ground.