Not precisely, but depending on the markings and the serial number, using the production records posted as a sticly above, we may be able to come close. Exactly how is your rifle marked on its receiver ring and side rail? Is it a long rifle or carbine?
There is a reliable way to date a Mannlicher-Schoenauer, at least on the commercial versions. I do not know if the military versions have the same proof requirements, and this data ONLY applies to Austrian Mannlichers, not the Breda ones. On the underside of the chamber you will find a number series like this 122345.19 That is a proof number identifying the unit as the number 122345th unit through the Vienna Proof House in the year 1919. I have seen this numbering standard on every Pre WWII Mannlicher-Shcoenauer I have had the opportunity to study.
Austria changed their proof markings after WWII, moving the proof data up to the side of the barrel and the receiver, just above the wood line, where the last two digits are the year of proof.