Educated at Harrow School, he was commissioned as a second lieutenant into the King's Royal Rifle Corps (KRRC) in 1915, and served with distinction with the British Expeditionary Force (BEF) in France during World War I. His nickname "Strafer" was a pun on the German war slogan Gott strafe England (God punish England). He was promoted to the rank of captain in January 1921, and attended Staff College, Camberley from January 1931. He was promoted major in July 1934, having been made a brevet major earlier in January. His service during the interwar period included a posting as adjutant to a territorial battalion, and a period of postings in India as a general staff officer (GSO2) and Deputy Assistant Quartermaster General.
Having been promoted lieutenant colonel in October 1938 to command the 1st Battalion, KRRC on its transfer from Burma to Egypt to become part of the Mobile Division (later to become 7th Armoured Division, the "Desert Rats"), Gott held a succession of posts in the division; he was successively chief staff officer of the division (General Staff Officer, Grade I, ranked lieutenant colonel) commander of the Support Group as acting brigadier, and General Officer Commanding acting major-general of the 7th Armoured Division.
While under Gott's command the Support Group performed well from the beginning of the campaign; skirmishing along the frontier from June 1940; conducting a planned withdrawal in September during the Italian invasion of Egypt, and during Operation Compass in December which saw the conquest of Cyrenaica and the destruction of the Italian Tenth Army the following February.
Following the arrival of the German Afrika Korps, under the command of Erwin Rommel, the Axis counter-attack in April, 7th Support Group, which had been refitting in the Delta, was called upon to stabilize the front and to reform the retreating forces, which was achieved at the Libyan-Egyptian border. In May Gott was placed in command of a mixed force to plan and conduct the ambitious Operation Brevity, which succeeded in re-taking the Halfaya Pass, but failed in its wider objectives. A subsequent larger scale operation, Operation Battleaxe, in which the Support Group also took part was also a failure and led to a reorganisation of the commands in the Western Desert which included Gott's promotion to command the 7th Armoured Division.
During the next major Commonwealth offensive, Operation Crusader, in November 1941, 7th Armoured Division was severely mauled by the Afrika Korps at the battle of Sidi Rezegh, but kept the field and contributed to the British Eighth Army's ultimate success.