Unless a seller can supply the original receipt, there's no way to know what year an ultra- vintage bag was made, especially anything that old. Year codes in Coaches only go back to 1994, remember. A 1965 bag wouldn't even have had a creed or serial number of any kind. The only way to even come close would be to look for styles featured in print advertising by Coach that can be dated to 1965, like old New York City newspaper ads or fashion pages.
And even that doesn't prove a particular bag was made in 1965. Except for Cashin designs, I doubt if Coach even changed their styles much, if at all, in their first 10 or 15 years of making handbags. I think you're trying to go back too far, unless you settle for a STYLE that was made in 1965, not a bag that was actually made that year. Maybe search this thread for "advertising"? There must be some old ad pages posted here somewhere.
ETA - If you can find one that fits your price range, one of those Cashin kisslock mini bags big enough to hold a cell phone might be a close enough style to 1965.
1960's minis from the Archives, I'm not sure if larger phones would fit the narrower kisslock openings though:
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