Yes, it was standard practice in the Royal Navy to start Cadet Midshipmen or Cabin Boys at a young age. See Horatio Hornblower. Any such practice can be abused if you have a power-mad or abusive Captain, but on the whole it worked out well.
It was also common practice for youngsters to start out very early aboard the trading schooners in Maine and other coastal ports, often sailing aboard their fathers’ ships and learning the family business.
Starting young at sea was not uncommon in most navies.
Lord Nelson was 13 when he went to sea for the first time,
Lord Collingwood was 12. John Paul Jones was 13 on his first voyage. Admiral David Farragut became a midshipmen at the tender age of 9. Admiral David Porter was 16 as was Admiral Yamamoto.
Hornblower was appointed a Mid in 1794, he was 18, a bit older than many of his messmates. Comments about Mids in their early and mid teens are sprinkled through the Hornblower books.