I'd have to disagree. Eastwood was extremely popular with millions of Americans who knew him from his Rowdy Yates days on "Rawhide". That's why Sergio Leone hired him for his westerns. From there it was an easy jump to Hollywood. I don't think he lucked into anything.
After considering Henry Fonda, director Sergio Leone offered the role of the Man With No Name to James Coburn, who proved too expensive. Charles Bronson then turned it down after describing it as the “worst script I have ever seen”. Third choice Richard Harrison also declined the role but pointed Leone in the direction of “Rawhide” (1959). Leone then offered the part to “Rawhide” star Eric Fleming, who turned it down but suggested his co-star Clint Eastwood for the part. The rest, as they say, is history.
Did you read the list of stars who turned down the role of “Dirty Harry”?