This is what Bae is wearing when he comes to live at the Darling’s house
This is what he is wearing on Hook’s ship
He is wearing a different shirt (see the bit of white in the second pic?)
Also the jacket in the second picture looks less beat up. In London his clothes were much dirtier and well worn.
Thus, I think Hook gives him new clothes and our timeline looks like this:
Bae comes to London and lives with the Darling Family
Bae sacrifices himself for Michael Darling and is taken to NL
Bae meets Hook and maybe becomes a member of his crew
Thanks, but he joins the family 6 months latter then what did do for 6 months in England ❓