The Luftwaffe was conceived as a very modern air force in the mid-thirties. Production of highly developed aero engines began immediately and as typical a number of specific functionaries were considered. Part of the construction of the Luftwaffe was strategic.
Firstly the widely accepted manner in which to win wars was by strategic bombing operations. The purpose of the fighter type was to allow bombers to operate over enemy territory.
The Luftwaffe added two entirely new elements to this general understanding, at least they were the first to implement them. One was a dedicated tactical air force. The other was a special operations transportation group (elite paratroops).

It is very important to understand this was not the typical thinking on air force deployment. Most militaries still regarded the air force as a singular entity and an extension of either Army signals or artillery departments (independent tactical operations). Roughly a third the entire Luftwaffe was designed specifically to work in close Army support, no other air force in the world followed this doctrine at the time.

The Luftwaffe had a relatively small number of short range tactical dive bombers (about 200) when the war began, supported by a strong force of high performance short range fighters. These would secure air superiority over the battlefield and allow what has become known as the Blitzkreig tactics which were so successful in Europe.

The main force was still strategic bombers, in keeping with thirties doctrine these were medium range, fast twin engine bombers with excellent performance and equipment. Another fresh idea was cast for their protection, Göring decided to implement a heavy long range fighter which would sweep deep into enemy territory ahead of the bombers to strafe airfields and attack enemy interceptors before they could gain altitude. He called this concept the Zerstörer, fielded by the Me-110 and one should note the only reason this wasn't successful in Britain was due to radar. Unfortunately the heavy fighter's performance at his stage of development was sluggish compared to single engine fighters and the Me-110 suffered heavily until it was reassigned as a ground attack warplane.

So in truth the Luftwaffe was very well conceived indeed for the period 1939-40. Its development implementation had been bluffed before then, and lived on the run following due to a basic industrial inadequacy for which Hitler had been ridiculously complacent in his foreign policy (crossing the bridge from politician to madman). But in 1939-40 the Luftwaffe was arguably the best air force in the world, hands down.

The Luftwaffe very nearly did win the Battle of Britain and certainly it was capable of it. Even with all the blunders and poor leadership at the top, it missed out on winning that war through simple attrition by about three weeks. The problem was getting accurate military intelligence at that stage, neither side knew how losses were affecting the other and the whole affair was a strategic guessing game. Göring didn't know if attacks on radar stations were having any affect, if more damage was being done attacking factories to the north or airfields to the south, how much damage he was doing to the British Merchant Fleet. None of it. If his men said they shot down 20 RAF fighters for a loss of 10, the RAF would claim 30 German aircraft were shot down for a loss of 5. Plus for most of the Battle OKL still thought strategic bombing and not fighter combat was going to win the battle, yet totally lacked any quantification of just how much damage a Heinkel or Dornier full of bombs really did to ground structures and loss of life. Prewar estimates of strategic bomber effectiveness were tremendously overrated all around the world, as can be seen by the sheer numbers of Allied bombers required to bomb modern industrial nations like Germany and Japan into submission at the end of the war.

The Luftwaffe also secured air superiority in the Mediterranean during the Balkan campaign and again at the beginning of the African one. Complete air supremacy was gained over the Eastern Front by the end of 1941. Air superiority was again attained in the USSR through most of 1942 and the tide only changed in early 1943 at the Kuban.

Sheer Allied numerical superiority harrassed the sporadic and limited Luftwaffe deployment in the Mediterranean, complicated by the tremendous efforts of Allied codebreakers in that arena. Entire flight plans of sluggish fuel transports were handed to interceptor squadrons, even their Me-109G and MC-202 escorts could do nothing, busy with Mark VIII Spitfire problems of their own.

Next the strategic arm of the Luftwaffe was completely abandoned by 1943 due to the pre-eminent need for fighters to combat overwhelming numerical superiority on every Front. Air superiority was and is, simply necessary to successful ground operations, this fact written into the new US military field manual of 1943. The Luftwaffe by late 1943 could barely even win local air superiority and was forced to abandon the air war utterly and do nothing other than Army close support and defend the Reich from bombers. There were just no numbers for anything else, and no strategic footing to work with.

Ultimately yes the Luftwaffe could easily have won the war, but at the same time it really had no chance. It was crippled by poor leadership at the top and German industrial capabilities and population limits, but was conceived brilliantly, even by Hermann the madman Göring (who tested a 140 IQ by the way).