The opening scene of Guardians of the Galaxy takes place in 1988 and while we don’t get an official age for Peter Quill’s grandfather, Gunn explains in a later tweet to another fan that Meredith Quill was 19 when Peter was born, and that Peter’s grandfather was only in his fifties at the beginning of the film.
There’s also the slight problem that if Captain America were Peter Quill’s grandfather, I think it would mean the Guardians of the Galaxy movies are part of a branched timeline, and not the one where everything else in the franchise is taking place.
This would mean grandpa was born probably in the 1930s, making him only a kid during World War II.