A Challenge For Knowledgeable Numismatists

I don't see any other way to know for sure other then to buy a 1975 mint set. The only other possibility would be if there were known die varieties that were attributed to only 1975. In that sense I am not aware of any known types.

How about getting a "free" 1975 mint set.

That's one way of knowing w/o buying one.

there are certainly die varieties that would determine the mintage year since quarter dies were only used for so long. the problem you'll run into is the lack of documentation about these die varieties since not too many numismatists studied them to the degree that they do today. you may have to get a coin set or open a bank roll from 1975 to get one.

Why not just collect the 1975 Cents, Nickels, Dimes from 1975. Put 2 of the 1975 Dimes and a 1975 Nickel together and you now have a 1975 Quarter.
Same with 5 Nickels, 25 Cents, 2 Dimes and 5 Cents and all from 1975.

As you said, the 1975 mint set would be your best bet.

Yes, the 1975 minted Bicentennial Eisenhower dollars have the variety 1 reverse and the 1976 minted ones have the variety 2 reverse. However, I do not know of any way to determine mintage year for the bicentennial quarter or half dollar.

I think it would make an interesting conversation to argue as to if all of the silver clad coins were minted in 1975.

I really don't know but a wiki reference suggests this:

"The first Bicentennial coins to be produced which were intended for the public were dollars, struck during February 1975.[26] The first for collectors were struck at San Francisco on April 23, 1975.[4] The San Francisco Mint struck the 45,000,000 silver coins first, striking eleven million sets in uncirculated and four million in proof, then began striking the base metal pieces."

Reference #4 is "Marotta, Michael E. "The Bicentennial coinage of 1976". The Numismatist, May 2001, pp. 501--503, 541--542."

If all of the Silver issues at San Francisco were minted before they started the base metal strikes, that would suggest that all of the silver issues were minted in 1975

My memory is not that great, but I think I got my Bicentennial Three Coin Silver Proof set as a Christmas present in 1975.

Sounds like an interesting project for a dedicate numismatist. Start studying the coins in the 1975 mint sets and identify die markers on the quarters and halves so that coins from these dies can be definitively identified as being struck in 1975. Once the die pairs can be identified (and published) then coins from those die pairs can be sold as 1975's and possibly even slabbed as 75's.