I think u mean to say "Not unless the baby was a month later(overdue)"
because as per the online calculator for the one night stand of Sep, 23, Due date should be around June 18. (40 week). if we assume that baby was month early then he should born around May 18. but for July 10, it is too post mature about 1.75 month.
Not unless the baby was a month early. Do you have access to that information?
She would have contacted you if she thought you were the dad, I assume.