There is a web site called "marlin manufacture dates", but it will only give you the year of manufacture, not an actual month and day. Seeings as you already know that it is an 1883 rifle, then you probably know as much as you are going to find out about the rifle.
1883.
your marlin rifle was made in 1957.
Your Marlin rifle was made in the year 1987.
1984.
1987
1985
1967
1893
With the serial number that you provided,your Marlin rifle was produced in the year 1979.
Your serial number indictes that your Marlin rifle was made by them in the year 1985.
With the serial number that you have provided,your Marlin rifle was made in the year 1996.
Your serial number indicates that your Marlin rifle was made in the year 1971.