First, the Kriegsmarine wasn't large by any means compared to the Royal Navy. August 1940 figures below:

I could keep going, but I don't have time to go through the vast number of British cruisers, destroyers, and smaller ships to compare to the small number of German examples (3 heavy cruisers, 4 light cruisers). Suffice to say the Germans were outgunned in the naval arena.

The biggest thing the Germans lacked where amphibious ships. The Germans had no landing craft for a large invasion. They planned to invade Germany during the fall of 1940, but this was at best a pipe dream without those assets.

The Battle of Britain was intended to be the opening phase of the invasion. The aircraft were intended to soften up the British and ease the invasion.

Needless to say this went poorly. The Bf 109E was a good match for the early model Hurricanes and Spitfires the British had at the time. However, the Bf 109 was quickly taken from the air superiority role it excelled at and given the job of bomber escort after the failure of the Bf 110. Being chained to the bombers rather than hunting the enemy fighters combined with the low range caused far too many problems to be viable. In addition the famous Ju 87 Stuka was a sitting duck without aircover and suffered heavy losses.

^(1) I have counted the Scharnhorst class as battlecruisers for this analysis. The Germans considered them battleships, but Garzke and Dulin, two famed naval historians, describe them as battlecruisers. IMO they were right in the middle and thus either title could work.

Leaving aside the "large navy" misapprehension, there is a comprehensive examination in Why Sealion is Not an Option for Hitler to Win the War by Alison Brooks. It's well worth reading for the full details. Just on the naval side:

• The naval part was derisory. "Block the east end of the Channel with mines and 14 torpedo boats (with 20 enemy destroyers immediately to face)." "... the barges would be adequately protected if the soldiers on the barges (travelling at night) 'Fired at unidentified ships'"
• they didn't have enough mariners to man the barges
• they really didn't have enough naval transport in general. Attempts failed miserably.
• the one exercise got fewer than half the men ashore on time unopposed in broad daylight
• many of the barges were river barges with low freeboard, so one British Tribal-class destroyer could have sunk them in a clock calm simply with its wake ... and good luck finding 30 hours of clock calm in the English Channel

This is leaving aside the horrible coordination with the Army (such as disputes about laying smoke and getting life jackets). And the 5 tasks that the Luftwaffe would have been given when in non-invasion times they had never been able to manage even one of them.

Let's start with your characterization of the situation first.

Germany did have a significant naval force, but it was a far cry from having naval superiority over the British fleet. German naval operations still mostly consisted of U-boat action against enemy shipping rather than outright naval engagements.

Amphibious assaults are very difficult. The logistic difficulties of getting all the men and materiel needed for an invasion force is massive, and that's before you consider the treacherous English Channel weather and the ability of British naval and air forces to disrupt invasion attempts. The allies D-day invasion required a herculean effort, and even that was only successful due to some crafty deception on the allies part and a slowness of response on the part of the Axis. Attempting an amphibious invasion without naval or air superiority would be an extremely risky endeavor even for an army as powerful as the third Reich's.

Despite this, there were early German plans for an invasion code named operation Sea Lion. Germany may have been able to overcome these difficulties and enact their plans if it were fighting the UK alone, but instead they locked in what would be the greatest conflict the world has ever seen with the USSR. That conflicted demanded far too many resources to entertain an invasion of lesser priority.

Hitler viewed the UK as a far lesser enemy in terms of power and importance than the USSR. He had hopes that the UK could be convinced to exit the war after the fall of France. He also underestimated British and specifically Churchill's determination to oppose him.

Air strikes were then as they still are today, the easier way to attack an enemy when the will or capability for a full invasion is not there. While luftwaffe commander Goering had early hopes that air power alone could subdue the British, that theory was quickly dispelled.

Source:

Rise and Fall of the Third Reich - William Schrier

Crusade in Europe - Eisenhower

The Kriegsmarine was not large, especially not in comparison to the Royal Navy. While only part of the RN could be present in home waters in 1940 on account of the need to check the Italian fleet in the Mediterranean and keep some ships in the Far East to deter Japanese aggression, it still comfortably outnumbered the KM. The advantage was somewhere in the region of 3:1 depending on ship type you are comparing. With respect to aircraft carriers, the British enjoyed a "Cannot Divide By Zero" ratio of superiority over the Germans.

The logistical difficulties facing the invasion have been discussed at length, and the Alison Brooks link posted by tim_mcdaniels is a highly amusing read on the topic. But suffice it to say that if the Allies had difficulty landing and supplying ~10 divisions in 1944 after years of extensive preparations with effectively unlimited resources, including the construction of artificial harbours, dedicated high quality landing craft and total air+naval supremacy, then you can imagine that the Germans are going to find it even more challenging to land and supply a similar number of troops in 1940 with scattershot preparations, re-purposed river barges for landing craft, disputed skies and a navy that cannot stand and fight. Even if the Germans get ashore in tact, they will not have brought their armour with them on the beaches (there are no Hobart's Funnies or d-day tanks for these landings). If they do capture a port successfully, the Royal Navy will simply blockade it. All resupplies that are accomplished by sea will come with an associated loss of (highly limited) barges and transport ships.

How would an invasion of the United Kingdom be possible, then? We don't need to speculate as to what the Germans believed must be required, we can look at primary sources. This is a link to Fuhrer Directive no 16. Hitler states that, in essence, the RAF must be completely destroyed. The Battle of Britain was launched with the explicit aim of achieving air supremacy and destroying the RAF. The logic behind this is quite simple - since the Royal Navy is vastly superior, the Luftwaffe must control the skies so as to be able to (hopefully) neutralise it, facilitate air resupply and initiate uncontested ground strikes on enemy formations. Air strikes will be especially important in ground combat because the Heer cannot bring tanks, trucks and heavy guns ashore on the beaches, essentially fighting with a level of equipment akin to paratroopers until they can secure ports to bring in heavy equipment.

Winning the Battle of Britain was therefore a necessary precursor to launching Operation Sealion, and the German High Command recognised this. Critically though, the invasion was on a timer. If the Germans could not invade while the British were reeling from the loss of heavy equipment after evacuating Dunkirk, and prior to American war materiel flooding in and strengthening their army, navy and air force, they probably never could invade, at least not without securing a massive industrial and resource base necessary to challenge American industry. This ticking economic-industrial timebomb is the direct motivation for the Nazi state to invade the USSR the following year, as described by Adam Tooze in The Wages of Destruction.

To add to the already excellent answers, I'd just like to put in one more point - Hitler was terrified of losing big ships.

Hitler was an army man, first and foremost. He didn't really understand naval warfare, but he understood the prestige of big battleships well enough, and he was loath to lose any of them. The loss of the Graf Spee early in the war had been bad enough without adding real battleships to the casualty list. The end result was that the Kriegsmarine's surface fleet was used incredibly cautiously throughout the war. The prime example is the Tirpitz, who fired her guns in anger all of once - to bombard shore facilities.

Apart from the excellent points already made, it wasn't just that the Germans had to get sufficient troops ashore in their invasion, they would also have to keep them supplied. The logistical tail would have been, if anything, more vulnerable to interdiction that the initial invasion fleet would have been to being halted. As has already been said, they lacked any kind of landing craft, or seaworthy supply craft that could land on open beaches. Again, as has already said, the invasion would have had to have at least a week of sustained calm weather for such unseaworthy craft to operate, and a week of calm weather in the Channel would be most unlikely! So even if the initial invasion had been successful, such success could not have been sustained.

Elsewhere in the thread, many responses have been about the naval disparity - which was huge (and not in Germany's favour, despite the assumption in the OP's question). But even if the British were somehow not able to stop the Sealion invasion with the Royal Navy, the slow invasion barges would have taken so long to get across the Channel they couldn't have done it all at night time, especially in the summer. I have read various places the barges would have needed between 20 and 30 hours round-trip. And thus much of that time would have been in daylight, leading to the next problem...

The Germans needed to negate the Royal Navy AND have air superiority. And that air superiority had to include over the invasion beaches. The RAF, even at the height of the Battle of Britain, had substantial reserves in the North, and these would, no doubt, have been deployed south in the event of an invasion.