Wyndham claimed to be the son of Colonel Charles Wyndham, a regular soldier who served in various Light Dragoon regiments of the British Army and was an ADC to the Duke of Wellington before becoming Lieutenant Colonel of the 36th Regiment of Foot. Wyndham had been born in 1833 on board the ship "Arab" in the Downs. He had begun his career at the age of fifteen, fighting in the Students' Corps during the French Revolution of 1848. He said that in July of the same year he was commissioned into the French Navy as a "marine ensign", a form of midshipman, before briefly serving in the Royal Artillery of the British Army from 1851 to 1852. After that, he had served until 1860 as a cavalry officer in the Austrian Army's 8th Lancers Regiment, before travelling to Italy to serve under Garibaldi. Wyndham said he had fought with Garibaldi at Palermo, Nuloggo, Rager, and Capua, at the last of which he had been promoted lieutenant-colonel, given command of a brigade, and knighted by King Victor Emmanuel, who had appointed him a knight of the Military Order of Savoy; and that was why he sometimes used the title of "Sir" in English. He had continued to command a brigade until on 8 October 1861, following the outbreak of the American Civil War, he had been given leave to enable him to offer his services to the Union.