Alms was born in Gosport, Hampshire on 15 July 1728, the son of John and Mary Alms. His father was said to be a servant of the Duke of Richmond. After a period working in merchant ships he entered the navy in 1740, joining the 74-gun , and by the age of 14 was rated midshipman and serving as aide de camp to Captain Charles Watson, of the 60-gun in the Mediterranean. He saw action at the Battle of Toulon on 22 February 1744 and was praised by his commander for his actions in the engagement. He then joined the 74-gun , serving with Admiral George Anson's fleet off the French coast. Anson's fleet engaged a French one at the First Battle of Cape Finisterre on 14 May 1747, winning a decisive victory and capturing a number of French warships and merchants. Alms remained in "Namur", and went out in her in October the following year to the East Indies with Admiral Edward Boscawen. "Namur" was one of three ship wrecked on the Coromandel coast in a storm on 12 April 1749, with Alms one of just 23 saved from "Namur". He was promoted to lieutenant on 14 May 1749 in the aftermath of the disaster, and was assigned to , a frigate returning to England in the spring of 1752.