The 1861 and 1862 Crew Agreements/Logbooks are at the National Maritime Museum, Greenwich UK.
You should be able to get hold of copies by filling in this form.
https://www.rmg.co.uk/national-maritime-museum/caird-library/crew-lists-agreements-official-logs-request-formHer 1863 Crew Agreements are at the Maritime History Archive, Memorial University of Newfoundland.
https://www.mun.ca/mha/holdings/viewcombinedcrews.php?Official_No=2666FORTITUDE, official number 2666 was built at Sunderland in 1804, she was still sailing at least to 1880, so a testament to her builders.
She was primarily a Home Trade vessel, IE, trading in UK coastal waters and maybe to the near continent. She would not be mentioned in Lloyd's List which only concerned Foreign going vessels but it may be worth checking in case she did sail to North America in 1863.
The University of Louisville, may have copies.
Given his status as apprentice there would be little about him in the Crew Agreements/logbooks but they may give you an indication on where she sailed. They should also mention when your ancestor left the ship.
Given the above plus her relatively small tonnage the chances of her sailing to the US are slim indeed. My guess his he deserted FORTITUDE and came to the US aboard another vessel.
Could you tell me where the information you have came from?