It's safe to say that, among the people currently shouting "LET US OUT OF HERE," one is going to be bad through and through and will pull the rug out from under any attempt the final people make to escape. They are playing by the Strictly Dominate Strategy in game theory which states that they will always make the move that benefits them, regardless of how it hurts everyone else. So making pals is not an option. You'll be tempted. The guy with the sad backstory or the single mom that just wants to get home to her kids is going to sound awful convincing. You'll chat with them, and you might even light a "we're all in this together" cigarette to share, but there's a decent chance, especially as people drop off, that they're going to be the ones that eventually leave you screaming behind a locked door.
However, Jigsaw is all about morality. He's like Freddy Kruger as a Sunday School minister. So, your best chance is to remain neutral at all costs. Your greatest gain will come from the appearance of trying to help other people make gains. Oh, that person "just can't take it anymore"? Scream encouragement from across the room. Jigsaw doesn't give you weapons, he makes traps. Thus, a good ninety percent of what's going to happen here is because someone got too emotional in either trying help out or get on top of the game, and fell into a bed of hypodermic needles. To remain thoroughly without needles, you must remain a passive player. So while you need to pretend to be an agent of passive optimism, always know that your part will come and you need to be prepared to be ruthless.
Give a metaphorical hand, not your literal ones.