Are your players experienced with sandbox play? Are you? If so, set one up, perhaps a subsector in size. They start off in a startown bar, looking for work, and go from there. Or, as I did it once, being released from their cells after a fight in a startown bar ended with the police turning up. Make friends in the cells overnight.
The only things I carry around these days when I'm planning to GM Traveller are maps and floor plans and a folder of NPC stats. Mind, I've played Traveller since it first came out, so while a book like 76 Patrons is within reach it's quite possible I've used everything in it twice before. If you're happy improvising, and your players are happy looking for their own hooks, that's a perfectly satisfactory way to go. Over time, you'll find out what sort of hooks they're interested in, what sort of things they'll do, and then you can build towards something larger behind it. They've constantly been interrupting the plans of some corporation? that corporation is backing a corrupt nobleman who is trying to become subsector duke, and the PCs are the only ones who can stop him. Find out his secrets, track down his k'kree mistress and obtain her testimony, and blackmail him out of the race. Or visit the local moot, participate in the parties, and make sure he doesn't win that way. Or... whatever they come up with.
Alternatively, go with a pre-existing adventure. There are plenty. Plane Sailing suggests anything from FASA, and I agree. I'll suggest anything from Digest Group Publications, though it's really hard to find. Or if you can find the reprints, the GDW CT adventures are worth a look. The Double Adventures would be my suggestion, since they're often quite short but have an interesting twist.