Question: Which event began first, the Western Allied invasion of Germany or the Battle of Aachen?

Context paragraphs:
Battle of Aachen: The Battle of Aachen was a major combat action of World War II, fought by American and German forces in and around Aachen, Germany, between 2–21 October 1944.  The city had been incorporated into the Siegfried Line, the main defensive network on Germany's western border; the Allies had hoped to capture it quickly and advance into the industrialized Ruhr Basin.  Although most of Aachen's civilian population was evacuated before the battle began, much of the city was destroyed and both sides suffered heavy losses.  It was one of the largest urban battles fought by U.S. forces in World War II, and the first city on German soil to be captured by the Allies.  The battle ended with a German surrender, but their tenacious defense significantly disrupted Allied plans for the advance into Germany.

21st Army Group: The 21st Army Group was a World War II British headquarters formation, in command of two field armies and other supporting units, consisting primarily of the British Second Army and the First Canadian Army.  Established in London during July 1943, under the command of Supreme Headquarters Allied Expeditionary Force (SHAEF), it was assigned to Operation Overlord, the Western Allied invasion of Europe, and was an important Allied force in the European Theatre.  The 21st Army Group operated in Northern France, Luxembourg, Belgium, the Netherlands and Germany from June 1944 until the end of the war in Europe in May 1945, after which it was redesignated the British Army of the Rhine (BAOR).

Normandie-Niemen: The Normandie-Niemen Regiment (Russian: Нормандия-Неман ) is a fighter squadron, later regiment (of three squadrons) of the French Air Force.  It served on the Eastern Front of the European Theatre of World War II with the 1st Air Army.  The regiment is notable for being one of only three units from Western Allied countries to see combat on the Eastern Front during World War II, and "Normandie-Niemen" was the only Western Allied unit to fight with the Soviet forces until the end of the war in Europe.

Allied invasion of Italy order of battle: Allied Invasion of Italy Order of Battle is a listing of the significant Allied and Axis formations that were involved during the Allied invasion of Italy (the landings at Salerno, Reggio and Taranto) 3 September – 16 September 1943.

Algernon Willis: Admiral of the Fleet Sir Algernon Usborne Willis (17 May 1889 – 12 April 1976) was a Royal Navy officer.  He served in the First World War and saw action at the Battle of Jutland in May 1916.  He also served in the Second World War as Commander-in-Chief, South Atlantic in which capacity he led actions against German and Japanese raiding ships.  He continued his war service as Flag Officer commanding 3rd Battle Squadron and Second in command of the Eastern Fleet and then as Flag Officer commanding Force H, the force which covered North African Operations, the Allied invasion of Sicily in July 1943 and then the Allied invasion of Italy in September 1943.  He spent the final years of the war as Commander-in-Chief, Levant, in which capacity he conducted naval operations in support of the Dodecanese Campaign, and then as Second Sea Lord, in which capacity he arranged the manpower for the campaign in the Pacific Ocean against the Imperial Japanese Navy.  After the war he served as Commander-in-Chief, Mediterranean Fleet, in which role he was faced with unrest in Mandatory Palestine, before he became Commander-in-Chief, Portsmouth.

Aachen Schanz station: Aachen Schanz station is a railway station in Aachen, Germany on the railway line Aachen–Mönchengladbach.  The station is located at the western end of the inner city, and is the station with the shortest walking distance to the historic center or the Aachen Cathedral.  Several bus lines to western Aachen stop here, including regional buses to Kelmis and Maastricht and the medical centers of the city (Luisenhospital, Franziskushospital, Alexianerkrankenhaus and Klinikum Aachen).  It is not a bus hub, but some lines stop at the southern end (Jakobstraße) and some at the northern end (Vaalser Straße), depending on the route of the line.

Western Allied invasion of Germany: The Western Allied invasion of Germany was coordinated by the Western Allies during the final months of hostilities in the European theatre of World War II.  The Allied invasion of Germany started with the Western Allies crossing the Rhine River in March 1945 before fanning out and overrunning all of western Germany from the Baltic in the north to Austria in the south before the Germans surrendered on 8 May 1945.  This is known as the "Central Europe Campaign" in United States military histories.

Siege of Aachen (1614): The Siege of Aachen took place in late August 1614, when the Spanish Army of Flanders, led by Ambrogio Spinola, 1st Marquis of the Balbases, marched from Maastricht to Germany to support Wolfgang Wilhelm, Count Palatine of Neuburg, during the War of the Jülich Succession.  Despite its status as a free imperial city, Aachen was under the protection of John Sigismund of Brandenburg, Neunburg's ally, and then rival, in the battle for the United Duchies of Jülich-Cleves-Berg.  In 1611, the Protestant population of Aachen had revolted against the Catholic city council and had seized power.  When the Holy Roman Emperor Rudolf II, observing the Peace of Augsburg, had ordered the previous state to be restored, the Protestants had allied themselves with the Margraviate of Brandenburg.  The unexpected arrival of a Spanish army at the gates of the city, however, caused the Protestants to lose courage and surrender Aachen to Spinola.  A Catholic garrison was installed and a process of re-Catholicization began.

Matthew Ridgway: General Matthew Bunker Ridgway (March 3, 1895 – July 26, 1993) was the 19 Chief of Staff of the United States Army.  He served with great distinction during World War II, where he was the Commanding General (CG) of the 82nd Airborne Division, leading it in action in Sicily, Italy and Normandy, before taking command of the newly formed XVIII Airborne Corps in August 1944, holding this post until the end of the war, commanding it in the Battle of the Bulge, Operation Varsity and the Western Allied invasion of Germany.

Arthur Tedder, 1st Baron Tedder: Marshal of the Royal Air Force Arthur William Tedder, 1st Baron Tedder, {'1': ", '2': ", '3': ", '4': "} (11 July 1890 – 3 June 1967) was a senior Royal Air Force commander.  He was a pilot and squadron commander in the Royal Flying Corps in the First World War and he went on to serve as a senior officer in the Royal Air Force during the inter-war years when he served in Turkey, Great Britain and the Far East.  During the Second World War, as Air Officer Commanding RAF Middle East Command, Tedder directed air operations in the Mediterranean and North Africa, including the evacuation of Crete and "Operation Crusader" in North Africa.  His bombing tactics became known as the "Tedder Carpet".  Later in the war Tedder took command of Mediterranean Air Command and in that role was closely involved in the planning of the Allied invasion of Sicily and then the Allied invasion of Italy.  When Operation Overlord—the invasion of France—came to be planned, Tedder was appointed Deputy Supreme Commander at Supreme Headquarters Allied Expeditionary Force under General Eisenhower.  After the war he served as Chief of the Air Staff, in which role he advocated increased recruiting in the face of many airmen leaving the service, doubled the size of RAF Fighter Command and implemented arrangements for the Berlin Airlift in 1948.  After the war he held senior positions in business and academia.

Supporting paragraphs: Western Allied invasion of Germany Battle of Aachen
Answer: The Western Allied invasion of Germany