Hamlet heard that his father was dead. He got on his horse and rode as fast as he could back home where he expected to find himself being prepared to become king. Instead, he finds that his uncle has taken over and his mother has joined against him. No matter how else we interpret her actions, we have to see that she has joined a coup d'etat against her own son. She may have good reasons, but Hamlet isn't likely to care what they are. The father dies and the son becomes king. It's as simple as that. Not the uncle. (I know that Denmark was not strictly an hereditary monarchy. Hamlet himself makes this clear, but I think he feels cheated of his rightful crown.)
Clearly, a lot of people conspired to make this happen. This is quite obvious. Hamlet suspects that his father didn't die of natural causes. He's suspicious from the start. And with good reason. He doesn't know exactly what his mother's part was, but it wasn't good. He's sure of that. And he has to wonder if she was fucking Claudius before his father died.
On top of that, a man who has always enjoyed his mother's nearly undivided attention suddenly finds himself pushed out of favor by her marriage to a man he despises and mistrusts. Hamlet has been pampered and protected by his mother all his life. His father was probably too paranoid to fully embrace the idea of an heir and he let his son idle away a lot of time at school. If he had been serious about making the boy into a king, he would have kept him near and taught him the ins and outs. But he probably feared that the kid would turn on him and maybe kill him. Seems like he was something of a prophet after all.
Gertrude was also not important to King Hamlet. He neglected her and never asked her advice or her thoughts on the events of the day. She had plenty of time to give her love and affection to her son. And she kept him close. Probably let him sleep in her bed. The boy had a too generous portion of his mother's love and too much exposure to her lovely, opulent, sweet-smelling, pampered queenly flesh. And all the while his father looked away and kept busy as warrior and a king. But why wasn't his son at his side when he conquered the lands of Norway? Why wasn't Hamlet trained to be a serious warrior king like his father? After all, everybody knows Laertes is a better swordsman than Hamlet.
In spite of all this, it's clear that Hamlet loved his father. It's not exactly clear in what sense this is true, but there's no reason to doubt Hamlet's sincerity on this point (even if we have to mix in his no doubt complicated feelings).
Hamlet also has to know that he is sort of responsible for his father's death. By being away at school and frittering away his time on intellectual pursuits, he was in no position to fill the power vacuum when it opened. As intelligent as he is, he must realize that if Claudius killed Hamlet Senior in order to become king, he must have conceived the plan because he was aware that young Hamlet didn't have enough street cred to convince the nobility that he was right for the job.
A man doesn't kill a king and conspire to leap over the rightful heir to the throne unless he's pretty sure a lot of other people are going to see things his way. And with Gertrude and Polonius on his side, he had to be pretty sure he would manage to get the job.
And all of this has transpired before the play even begins.