So one of the questions I always like to ask of vets is what things you do to make the initial meeting of the party feel smooth and natural? Everyone knows "you all meet in the inn" but I'm always looking for a good kick off for the party that automatically gets all the players to gel and feel like they know each other or drives them together in a way that will form long-lasting bonds?
There is also the party is joining a caravan, party finds themselves locked away in a dungeon, etc. I don't have a lot of great ideas here. But one campaign start I love is to use a funnel.
For example, say the game is D&D 5e. Have each player role up four characters. They only get a background and appropriate equipment for that background. No classes yet. Have them all be from the same village or town. Or perhaps they are all part of the same military unit. Or they all have roles in castle or keep. Or they are all travelling in a large caravan for mercantile, religious pilgrimage, they are refugees, or other reasons. Have each player give a bit of light background for each of their four characters and how they related to each other and perhaps other other players' PCs as well. Good to have spouses, siblings, lovers, childhood friends, mentors, parent-child and other relationships represented.
Whatever set piece, their town/caravan/stronghold/etc. is attacked. Their should be huge losses of NPC lives and it is expected that each player would have one or more of their PCs dies.
From the surviving PCs, have each player select one and finish creating a level 1 PC of that character. Perhaps with some role-play or off-the-screen backstory.
Now you have a group of PCs emotionally invested in getting revenge, seeking justice, etc., against your campaign's first antagonists as well as a shared background and origin story to explain how and why the party came together.