"Welcome to the wasteland... now give me your stuff!"
Often, the opening moments of a game are the most memorable. Even though it's rather brief, I love the opening of NEOScavenger and the first Dogman encounter ("WTF is going on?!"). I love the moment of stepping outside, dazed and half naked, to see the overgrown world around you. I love that you get a little "cutscene" for the first town you visit... seeing ruins that suggest something terrible has happened to the world.
Something I'd like to see added to the early game in a similar way is an "encounter" (like the cryo facility Dogman multiple choice one) for your very first human meeting. Realistically, this would be a pretty major moment for the player's character; after waking up in a Cryo Facility with a Dogman breathing down his neck and the world outside in ruins, he might be forgiven for thinking he was the last human alive until now.
I think it would be cool to "introduce" fellow human survivors with a special encounter for your first one. The fact that (so far) everyone out there is hostile to you could be explained in this; you could have the choice to attack first, or to try and talk and be attacked by that initial desperate scavenger you stumbled across and hoped to get information from. Either way, the tone is set: it's everyone for themselves in this new world, and finding out you're *not* the last person alive is in fact not really such a good thing!
I also think that the player's first human "kill" (likely after the previously mentioned encounter ends!) could have a similar (text-based) mini-cutscene... a dramatic moment when you realize that you've just killed a person for the first time in your life, but that this is your new world.