Everyone groans when the question of Operation Sea Lion is raised for the umpteenth time, but then lots of people pile on with comments anyway--because the subject is endlessly fascinating.
The Germans could not have pulled off Sea Lion without starting to plan it and building a huge fleet of landing craft, more surface warships and many more planes as of about 1936. But if they had started doing this, it would have freaked out the Brits and they would have started seriously preparing for war, including building up their army, bringing new fighter planes on line more quickly, etc. (think 3,000 to 4,000 Spitfires and Hurricanes by the spring of 1940).
Butterfly effect? The Brits are vastly better prepared for war in 1939 and would already have taken a hard line against German expansionism, like not allowing them to take over Austria and Czechoslovakia. And the Germans, by putting their resouces into preparing to invade England, would be less well prepared for a war in the low countries and northern France. And Mussolini would stay out of it, since the Brits would have some scary tanks and planes, lots of them, in Egypt.
But the idea of preparing in 1936 for an invasion of England is so screwy that even Hitler wouldn't have chosen that as the best allocation of resources. So no, the only way Sea Lion could have worked OTL is as a bluff to get the British to sue for peace BEFORE any invasion was attempted. That might have happened if Lord Halifax had replaced Chamberlain. So the question becomes a political one rather than a military one.