It was the gravest of mistakes, and even though they could not have been aware of it basking in their rapid victories, there could be no other outcome, but failure.
So confident was the German high command and it's glory seeking leaders, after the taking of Austria, Czechoslovakia, Poland and France, all of whom were defeated by bullying, propaganda or lightning war (blitzkrieg) and especially the Luftwaffe chief, Hermann Goering... they had overlooked several severe flaws in their strategies.
Crossing the channel, was nothing like crossing an invisible line on a map into the Europeans countries, no sir, this would be much much more of a challenge and prove their fallibility in no uncertain terms.
You would think after the failure to annihilate the B.E.F . and the remainder of the French army at Dunkirk
allowing hundreds of thousands to flee to the Island fortress, someone would have stepped up and clued in. In their zeal, basic facts and battlefield principles were swept aside and completely ignored.
For Operation Sea Lion to succeed, not only would the RAF have to be immobilized or eliminated completely, but the powerful Royal Navy as well.
In the Battle of Britain, the Germans severely underestimated the ability of the British to meet the challenge and in fact, even though the Luftwaffe was proven and confident, it was in essence a tactical air force designed primarily as ground support for the Army. It's best fighter plane at the time, the Messerschmidt ME (BF)109 was severely hampered by it's design as a short range battlefield fighter. It had neither the range or endurance to venture far into the British realm, in support of vulnerable tactical bombers like the Stuka, supreme in Poland, but pigeons for the Hurricane's and Spitfires.
Ultimately the German war machine would grind itself into submission, throwing itself against fighter command, which aided by early warning radar, could concentrate it's limited fighter force against the main thrust of the Luftwaffe as they crossed the channel.
Not only did the German's fail miserably to provide the require air supremacy for a cross channel invasion, they had lost against the growing strength of the British, even before the battle was over. Without total control of the air over the British Isles by the Luftwaffe, they had no way of protecting the German fleet from the much stronger Royal Navy. Even had they been successful in gaining tactical control of the channel, they would still have to deal with the world's largest and best trained Navy. The Royal Navy, and Britain itself would fight to the bitter end to keep the foe from the shores of Dover and the streets of Piccadilly.
In essence the invasion would never take place without the elimination of British fighter command. Something the Germans failed to achieve.