If you give the Germans 20/20 hindsight a few years in advance, that would be enough for them to have a chance at success. No guarantees, but if they come prepared with longer ranged fighters, proper landing craft, a few dedicated marine divisions, a navy that focused more on well-armed destroyers, E-boats, and U-boats than the cruisers and battleships, Japanese-style torpedo bombers and tactics, etc, they'll at least have a decent shot at it. It will be a close-run thing no matter what.
I think it's possible for Germany to prepare itself in such a way without crippling itself for the land wars in France and elsewhere. If they decided to prepare for it by some form of Plan Z, that would obviously take enough resources to handicap the army significantly, and would definitely antagonize Britain. Building the navy of smaller ships would come across as less intimidating, since it looks more like a Baltic fleet than one that will challenge the RN at sea.
Largely agreed, if the military command benefit from 20/20 hindsight, it is possible to win, but far from certain. If Hitler had not tried to invade Norway, I am sure many historians would say the Norway operation WHILE preparing for an attack on France would never work. But in war, strange things sometimes do work, and long-shots do payoff. After all, it was a fairly low ranking artillery commander that almost lead France to conquering Europe and building a lasting empire. If Napoleon had been shot and killed early in the war, no one would have looked at his resume and said this is one of the greatest land Generals in history who happened to be shot before he took over a major command. All it would really take is one naval leader who Hitler would listen to who was a quality leader. I suspect a Admiral such as Halsey, Nimitz, or Yamamoto could have prepared a plausible plan starting with resources available to the German Navy in 1936. The only POD required is finding some Brilliant leader in the ranks of the Navy. Below is my list of relatively cheap improvements to the German amphibious command from low cost to higher costs.
1) Have a team of 3 to 6 field grade naval officers actually contingency plan for this operation in 1936. A lot of problems that are hard to solve at the last minute are easy to solve earlier on. (Almost zero marginal costs)
2) Test the U-boat pre-war at realistic (full) operating depths. Many U-boats had to go in for overhauls to fix minor issues at the start of the war. (Actually negative marginal costs since many subs will be built right the first time instead of having to have a major overhaul after construction)
3) Instead of just working with the Soviets training new Luftwaffe pilots, have a small cadre train with the Japanese Naval aviators. (Low marginal costs, how much does training 40 pilots at Japanese naval schools cost?)
4) Develop pro-type landing craft complete with blue prints. Develop a plan for crash production of enough to make the plan developed in step 1. (Low marginal costs)
5) Realistically test the torpedoes, and fix the flaw in the detonator pre-war. (Low marginal costs, this involves a design and testing team doing there job correctly.)
6) Develop better Naval codes. (Moderate costs, because it would have to be developed and deployed fleet wide, but dirt cheap compared to losing ships or building a battleship.)
7) Instead of developing all the torpedoes and naval planes from scratch, but the equipment from Japan. While the Germans may or may not have had trouble sinking capital ships with air power, the Japanese did not. (Moderate costs)
8) Designate either one division or one corp to receive introductory amphibious training. Having the regimental, divisional, and corp level officers study issues related to amphibious warfare pre-war improves capabilities. (Moderate costs, but this training might reduce the effectiveness of these divisions in France due to opportunity costs.)
People like to focus on only on England, but Germany would have benefit from better amphibious options in Norway, Crete, Malta, Gibraltar, and possibly the invasion of Russia. A small invested in better amphibious operations would make the British High commands life much harder. None of these are the magic bullet, but some preparation for amphibious operations would have made sense and been cheap, or in some cases almost free. I do agree that if the POD is post-France surrenders, it is very hard to impossible to then throw together a major amphibious operation against one of the strongest Navies in the world.
If all of these had been done, then the situation looks much better for the Germans. Instead of lets do this ad hoc, they have a well prepared planned to discuss, and will be able to determine if it is really possible or not. The British will have lost a lot more ships due to more subs, better torpedoes, and less intelligence, including some additional capital ships. The Germans also had a landing force that does not have to start training up from square 1.
So in one sentence. Sea Lion is almost impossible if the POD is in mid 1940, but becomes possible but hard if the POD is a few years before.