I *tried* to sandbox, but my players were horribly unintuitive..
That said, if they had any heads on their shoulders, and were able to think on their own, I would do the following:
Cook up some really basic non-combat encounters of sorts. In some cases, players will tell quest givers to fuck off. In other cases, players will go with it.
In order to buy myself time to write up more story, I would throw an encounter or two at them. Most encounters that are on a tactical scale tend to chew up a good hour or so of game time. If I'm using Battletech, and the players are as utterly green as they were the last time, that's about one to six hours, depending on whether it's one-on-one, or four on four. It only takes that long because shit gets bogged down by rules arguing, rule-forgetting, and players being ignorant and fucking around on DSes or iPhones.
Wrap up session, See you next week, Begin thinking up plot branches and complications that could occur due to the player's actions.
Also, be sure to not waste time making full NPC character sheets. Just ad-lib a few numbers after you've gotten used to the system. Estimate chance "Scales" according to what you know about the system. For example, In Mechwarrior 2nd edition, I knew that a 10+ to hit meant a character pretty much sucked, a 8+ is green, a 6 or 7+ is regular. 5+ is pretty much a specialized skill for most characters, and anything less than 3+ makes them elite at something. After I learned to ad-lib using numbers like those as rough guidelines, over writing up massive sheets with stats and background for characters players may never see again, I saved myself a world of time.