Conway presumably spent his early life at the Dutch garrison town of Brill, where his father, Sir Edward, was lieutenant-governor. Although he enjoyed a taste of higher education in England, he was ‘bred a soldier’, probably gaining his earliest military experience as a volunteer in the Netherlands, where he ‘perfectly learned the rudiments of warfare’.
At the 1624 general election, Sir Edward requested the lord warden of the Cinque Ports to supply Conway with a seat at Rye. However, Lord Zouche had never heard of the young man, and instead nominated his elder brother, Sir Edward Conway II, who also secured a place at Warwick. Once a fresh election was called at Rye, their father wrote to the borough on Conway’s behalf, explaining the mistake, and promising ‘in every point to be answerable to you for his care and diligence in serving you’. Conway attended the election on 28 Feb., and was sworn a freeman. Despite the sustained effort to get him into the Commons, he left no trace on the records of the last Jacobean Parliament, even though he and his fellow Rye Member were instructed to lay before the Commons a bill to secure control of the Dungeness lighthouse (situated at the mouth of Rye harbour).
Thanks to his father’s influence as a secretary of state, Conway was commissioned in June 1624 as a captain in the regiment sent to the Low Countries under the command of Lord Willoughby of Eresby and Sir Edward Conway II. He was also knighted a month later, along with his uncle and namesake, Thomas Conway of Ragley, Warwickshire. However, the military stalemate in the Netherlands gave him little scope for action, and in mid-1625 he expressed frustration that a shortage of funds was preventing a major offensive.