Allegedly snapped at a London party in 1957, when Cary Grant was around 53 and Sean Connery was 27. Connery was then filming (or had just filmed) Another Time, Another Place with Lana Turner. His hair was still reasonably thick, or at least not thinning.
I don’t believe that story about Bond producer Albert “Cubby” Broccoli offering the 007 role to Grant roughly four years later, sometime in early ’61. The 57 year-old Grant had reached his dashing physical peak when he shot North by Northwest in ’58, and was at least ten years too old to play a hotshot British agent — Grant himself believed this. Plus Broccoli wanted Grant to commit to five Bond films, a proposition which Grant immediately declined.
Connery was hired to play Bond sometime between the late summer and early fall of ’61. Filming on Dr. No began in Kingston, Jamaica, on 1.16.62. It opened commercially later that year. Connery made it through the first two films without a full toupee, but was forced to wear one for Goldfinger.