I actually have a theory about this. (Big surprise, huh? I have a theory about literally everything.)
Please keep in mind that Sam had lived without Dean twice before, once for the 6 months in Mystery Spot and once when Dean was in hell. Both times, Sam drove himself half-insane and went off the rails to save his brother. In Mystery Spot, he was willing to kill someone who could have been Bobby if it meant he could bring Dean back to life. When Dean was in hell, he tried to make a deal, tried to do anything he could to rescue him. When he that didn’t work, he started destroying himself to get revenge on Lilith.
That brings us to season 8. Dean was gone again but this time Sam had no one to help him, no one he could play “let’s make a deal” with, no one to turn to. No Bobby, no Cas, not even Ruby.
I think all Sam wanted to do right then was curl up and die. It’s possible he was suicidal when he hit that dog. Hitting the dog and meeting Amelia ended up being a lifeline to a drowning man. Amelia had just lost her husband and seemed to feel the same way. So they clung to each other until Don came back to life and then Dean came back to life. (ha! Don…Dean… I just noticed how much alike those names are. PARALLELS.) Then they went back to their other lives. Although apparently Dean was more important to Sam than Don was to Amelia because she was willing to leave him for Sam.
My point is that I kept thinking they were going to explicitly state that Sam had been depressed and hadn’t wanted to go on living, but they never did. The closest we got was when the boys were talking to Brick Holmes’ wife in episode 8×03 Heartache and she was talking about how he died:
MRS. HOLMES: I don’t think he could bear the thought of life without me. That’s why he drove off that bridge.
Then Sam shoots a furtive glance at Dean and gets very nervous.
So that’s my theory and I’m sticking to it. Hope that helps, anon!