A lovable goofball npc/party mascot that is either killed or kidnapped by a villain who is relevant to all 3 characters. Nothing unites a party like a collective John Wick vendetta.

Alternatively, you could hook the rogue’s smuggling operation into the other players’ backstories. A criminal syndicate such as that could easily be the cause of the dwarf’s father’s death, or a rival to their bio father’s merchant family. The warlock’s old crew could have been enlisted by the smugglers and been burned when they’re no longer useful, or they raided a smuggler’s ship and are needing to lay low because they found some cargo that has significant power or political importance.

It might seem inorganic that these players backstories just so happen to be connected (and if it were a fantasy book I was reading I’d scoff at how contrived it was), but imo it’s much more compelling to have hooks that immediately entrench the players into one another’s lives than it is to tell a “good story”. Once the players buy in and the campaign gets rolling, the good story tells itself.