The first effort to get rugby sevens in the Olympics was back in 1931.

A Galashiels man, then residing in Canada, wrote to the International Olympic Committee proposing that rugby sevens be included in the 1932 Summer Olympics at Los Angeles.

Mr. W. Hastie Cochrane of Esquimalt, British Columbia proposed that the Five Nations international teams – Scotland, Ireland, England, France and Wales should be included and all compete for the Olympic title. [Scotland, England and Wales frequently had separate national teams in the Olympics; e.g. the Scotland hockey team won bronze medals in London 1908; and the Scotland cycling team came fourth in Stockholm 1912.]

The Sports Technical Director of the I.O.C., Mr. W. M. Henry, replied to Mr. Cochrane:

“I have just received your very interesting letter regarding the possibility of an exhibition game of seven-a-side Rugby football for the 1932 Olympic Games. I am very sorry to say that the powers of the Working Committee are limited to two exhibition sports, and American football and Lacrosse have already been chosen for these events in 1932.”

Mr. Cochrane also noted that rugby sevens was played with success in Montreal and the sport might also spread to the U.S.A.
https://www.britishnewspaperarchive.co.uk/viewer/bl/0002784/19310924/088/0006