So, I find that it's a good idea to assume some initial connections between the adventurers. They don't all have to know each other, but at least some of them should have some sort connection to the others. It's not a bad idea to establish before the game that everyone, even if they don't know all the other party members, has some sort of mutual connection to at least one other player and preferably two. You can let the individual players work out what those ties are - two characters extended school together, two are related, two are former/existing lovers, two knew each other as children, or whatever.
It's also pretty important that everyone have some preexisting motive to face danger and risk. You can't have a party risk adverse anti-social types whose response to danger is to borrow into a lair and not go anywhere. Everyone needs a motive to be a hero. In D&D, it's probably a pretty good idea if there is a central alignment to the party and everyone is within about 1 step of that unless you have very experienced and mature players that can handle a mixed motive party AND you aren't doing a sandbox. Sandboxes require everyone's motives be aligned pretty closely. And all your players should be told about these expectations before they show up with characters.
Thirdly, they do all need to start somewhere. It's easiest if the starting point is a public place where it is easy to explain everyone's presence, and it can be a tavern (but need not be). Examples of public places can be a university (they are all students), a temple (they are all polytheists worshiping some deity), a festival (they've all come to enjoy or participate the festival in some fashion), a place of business (they are all bidding at an auction, or at least accompanying someone who is), or a harbor (they are all expecting something delivered from a particular ship). However, you can do a private location as a starting place as well - they've all been invited to a dinner party by a mutual acquaintance, they are all servants of a local lord and he summons them about a problem, they've all responded to be broad sheet from a veteran mercenary who is forming a mercenary company for some venture (like guarding a caravan), or they are all aboard the same ship sailing to some destination.
Third, if you are going to supply the motive to the story, rather than run a sandbox, start with a bang. If the players aren't already all on the same page, something so big and important needs to happen that responding to it becomes every PC's #1 priority regardless of their motive. And I do mean a big bang. Even if you plan to slow down in chapter 2 or 3 and start building back up with slow rising action, chapter 1 should be huge shattering event of historical importance. Disaster should happen right in front of their eyes. Kings should die, cities should fall, volcanoes should explode, meteors should fall out of the sky and blast half the landscape out of existence, old gods should rise, or whatever. Whatever should happen should be so big and so important that everyone's motive should be survival and dealing with this thing. After that, you can start introducing your plot threads in that context of 'the big thing'.