I was just thinking about it a few days ago and it hit me, Joel became hard and almost emotionless because of Sarah's death. If she hadn't been killed, would he have been able to do the things he did to survive? He told Ellie he had been on both sides of ambushes, and judging by the conversation he and Tommy had just before the power plant was attacked, it seems very much like he spent some time as a hunter, killing people and taking their stuff. But the question is, would he have been that way if Sarah hadn't been killed, or would he have been softer and he himself have been killed?
Doubtfully. Joel would have had someone to care about, and because Sarah was pretty innocent, he'd kept more of the humanity he had. Of course, he would've gotten to a point where he'd kill without remorse to protect Sarah...
...just like he protected/killed for Ellie. But it would have taken longer to get to the point where Joel was after Prologue, emotion-wise.
I have acquired the grade of Master in The Last of Us story/character/game knowledge as I have played it through 9 times.
... I have no life.
“The worlds been hard on us…hard on him. Joel’s done some terrible things. He tells me that on this journey, you either hang on to your morals and die, or do whatever it takes to survive.”
— Ellie (The Last of Us)
I think he would have been just as ruthless in order to protect his daughter. Even in the beginning before Sarah's death he doesn't want to pick up that family because Tommy hasn't seen what he has seen. Granted, the start of the infection is a lot different than twenty years later, but I still think he would make the same tough decisions to protect himself and whoever he cares about.
Plus even listening to the cutscene with Joel & Tommy implies he had to do some terrible things in order for him and his brother to survive.
You never know though. I think at the very least Joel would be less experienced than he is now. But no matter what you'd still have to fight against infected and people who will kill you for your supplies.
I think he would have survived, maybe even with more force given his need to protect his (still alive) daughter. For sure. We know it was in him to begin with, in the car with Tommy he was totally okay with leaving a family on the side of the road with his daughter's safety in mind. Joel is just that kind of person, to do anything to survive.