In a later post I will address the novel's themes and characters and compare them to those in Pride and Prejudice. For the time being I will use the historical record to evaluate Lady Russell's near-fatal judgment of Captain Wentworth's career prospects, which occurred six years before the novel begins.
As a preface, Jane Austen was well acquainted with the Navy and its officers. Two of her brothers were post captains who rose to become admiral after her death, and the description of naval occurrences, though not in the foreground, is done carefully by someone who knows what she's talking about.
Captain Wentworth was not born at a lucky time or at least, he didn't advance in his career at a lucky time. The best years for navy men were the early years of the revolutionary wars, the 1790's, when British dominance on the sea was less secure and there were ample prospects for distinguishing oneself in action and gaining a fortune in prize money (Austen's older brother Francis was made lieutenant in 1792, just as war was declared, and rose to become Admiral of the Fleet). Captain Wentworth was not a Captain in those 'lucky' years before Trafalgar, and was probably not a lieutenant for most of them. In 1806 he was a Master and Commander, an officer qualified to command small 'unrated' naval vessels such as sloops of war. He was promoted due to his role in the British Victory off Santo Domingo earlier that year. This victory was the last time British ships of the line met French ships of the line in a fleet action in open water. After Santo Domingo, the bulk of the French navy remained bottled up in Brest, Toulon and other ports, blockaded by British squadrons. While this was good for Britain it was bad for the careers of her sailors, who now had extremely limited opportunities to distinguish themselves.
The Battle of Santo Domingo by the great sailor/artist Nicholas Pocock. In the foreground the British Northumberland (74, right) engages the French Imperial (120!, left). The Imperial was driven aground and later burned.