I don't know that I've EVER run a FIRST adventure as "you get hired to..." just because of some of the issues people have mentioned.
Instead, I have done other things such as:
1) you have arrived in x village/town and are now at the Inn. You are here following rumors that there is a dungeon nearby... what do you do?
2) you are in the market when you hear a horrible crash, and a roar, and then screams. You realize a large pit has opened up in the center of the market square, and a mass of black clad humanoids are leaping up out of it, grabbing and attacking people... what do you do?
3) you are all friends who grew up in x village and now goblins have begun raiding farms. The sheriff has a standing reward out for them. You're broke. You can hire on as caravan guards, hunt goblins, or go get a regular job... what do you do?
Note the requirement that the PLAYERS decide how they form a group, and why. That's THEIR job as PCs, not mine as a DM. If they decide that half of them become guards and the other half hunt goblins, well, then they'll meet a day outside town, as one group tracks goblins and the other is attacked by them... and the one who gets a regular job gets to roll up a new ADVENTURER PC!