Maybe I missed something. Who was the woman Gene was in bed with in the beginning of the movie? It wasn't his girlfriend from California. Was she just a booty call? Because they really never developed her character. Gene is supposed to be this stand-up guy, who's faithful and committed to his doctor girlfriend who lives in California. However, he's going balls deep with an unrelated woman. Are we just to assume that Gene got an inch and scratched it?
That could well be the case, but it could also be something more than that. Sex isn't always just for pleasure (though of course it's very pleasurable), but often for closeness & comfort, to stave off loneliness, fear & grief. Gene is about to see his father again & reveal that he's moving across the country to start a new life. All the memories & pain of his childhood are hitting him with full force, because he already knows how his father will react. Yet he's still hoping against hope to connect with his father, perhaps even find the love from & for his father that's been lacking for all of his life.
We don't find out much about Norma, the woman he sleeps with at the beginning of the film. Maybe she is just a pickup to scratch that itch you mention. Or maybe they know each other from the past. Or maybe it's a mutual moment of staving off loneliness. We just don't know. For me, sleeping with Norma reveals the depth of his dread & uncertainty, and his need for reassurance before facing his barren relationship with his father for what may well be the last time.