This is fairly well researched family, and I would suggest you are not going to be able to find something which doesn't exist.
Certainly, without an actual reliable source, his birth date needs to be changed to a reasonable estimate. I am not sure why you say he may have been born earlier. If he was married in 1594, then he was most likely born later than 1560 with a range of 1565 to 1574 being the most likely. If he was a son Edmund Scott of Rattlesdon, as is likely, then he had siblings born 1567, 1569, 1571, 1573 and 1576, eliminating most of the date range.
The reason to think he was not born in Rattlesdon is that we cannot find his baptism, but this is not unusual for early parish records to be able to find some but not all of a family group. The fact that his father Edmond Scott was a church warden, does give some credence to the idea that he night have come from elsewhere. Church officials were fairly mobile in this time, being trained in one place in then assigned to various parishes.
It is clear to me that, without better evidence, his birth should be changed to "About 1565, probably in Rattlesdon, Suffolk, England."