There two ways that someone can determine the “Made On” date of their Remington firearm.
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REMINGTON MANUFACTURING DATE CODE stamped on LH top rear of barrel, 2 or 3 digit, (month first, year after) these will normally only be the last letters as seen below, The factory says all barrels are date code stamped, well I have found some that are not, or if they are, are so erratic stamping that trying to decipher them is impossible. Both were taken off Remington 760s, with the one on the left, a 30-06 that I bought new October 10, 1954. The one on the right again a 30-06, but with a shorter barrel that I made into a knock around quad rifle with pivot mounts.
(*) On 8/9/99, they stopped stamping the barrels with the date code.
To determine the date, you need to look for the letters stamped on the left side of the barrel. The next letter (possibly 2 letters) will give you the year code.
Please note that during the years of 1999, 2000, & 2001 (highlighted in red above), Remington did not stamp the date code on the barrels.