I start my sandboxes (campaigns) by giving the players a sheet or a few sheets of information that describe what their character knows about the world. It usually includes a rough map as well. Part of it is just common knowledge that all of the players know. Some is player specific. Overall it covers things like the known factions, the local politics, important people, rumored locations or items of note, stuff like that. It also includes around a dozen rumors that are a mix of fact, fiction, and in between.
The next question to me, is how do the characters themselves start? Mine is set in a village and they are all from that village. So they already know each other. I allow them to create details for some relationships with some of the other villagers, but they have to be friendly with the other characters. While I can, and have, come up with specific reasons for the characters to be together at the start, I like them to provide a lot of input into that now, since they are from the same village.
Now in my campaign, everybody has at least 3 characters. They can come in and out as they desire (when appropriate). It also allows us to jump between multiple ongoing groups depending on who can make it that week.
We also do character creation at the table again. Backstories and personalities are developed right there (we've also gone back to rolling stats in order, and I have some things like traits that give some minor bonuses and helps with potential personalities). The player will develop things a bit more, and we also work on this together outside the session. The first half dozen or so sessions I allow a lot of flexibility for changing things around to what they are comfortable with.
But, since they have multiple characters, it also provides opportunities for them to cover a lot of bases in class and personality.
Since I run in the Forgotten Realms, I also encourage them to read up as much as they want on the world. Not everything published is exactly what happens in my campaign, but it provides a good amount of shared knowledge up front that I don't have to write.
Sometimes, maybe not the first session, but a few sessions in, there will be an event that draws the village together (orc attack, giant attack, etc). Everybody has to serve in the militia and is trained (and provided a weapon) by the town (10 days three times a year). So we can also start with one of those stints if we want.
The idea is to always give them far more options than they need so they feel like they are really in charge. Since I don't know what will interest the players (or their characters), it's a mix of politics, intrigue, local and regional news, local relationships, dungeons, and rumored treasures. That way they have pretty much free reign to choose what kind of adventure they are looking for.
Downtime activities also come into play more, which is great because it helps them come up with goals for their characters other than just exploration and adventuring. The campaign time-line continues for the off-stage characters in time with the on-stage characters. I'm looking at expanding the group by potentially running some drop-in games at the local store. If I have time, I'll let my regulars know, and I'll see if there's anybody at the store interested in playing. I'm hoping that some of my regulars will be able to make it to some of these drop in sessions, because I want to foster some cross-campaign characters between multiple groups and see where things lead!