Why doesn't Hamlet react angrily immediately after his father's murder?

Hamlet does not react angrily immediately after his father's murder because he does not actually know that his father has been murdered. Hamlet does not learn until act 1, scene 5, when he speaks with his father's ghost, that old King Hamlet was, in fact, murdered, and by the king's own brother, Claudius. Hamlet's father's ghost tells him,

'Tis given out that, sleeping in my orchard,A serpent stung me. So the whole ear of DenmarkIs by a forged process of my deathRankly abused. But know, thou noble youth,The serpent that did sting they father's lifeNow wears his crown. (1.5.42–47)

In other words, the ghost says that everyone in the country has been told a lie: that he was killed by a snake that bit him while he was asleep in the orchard. In truth, that "serpent" is actually the man who now wears the crown of Denmark, the dead king's own brother, Claudius. It is only at this point that Hamlet can respond with anger to his father's murder because he's only just learned of it.
Hamlet is angry at the start of the play, but his anger is the result of his mother's hasty remarriage to her own brother-in-law. When he speaks to his friend Horatio, he tells Horatio, sarcastically, that

The funeral baked meatsDid coldly furnish forth the marriage tables.Would I had met my dearest foe in heavenOr ever I had seen that day, Horatio! (1.2.187–190)

In other words, he caustically jokes that the leftovers from the funeral fed people at the wedding because the wedding followed the funeral so quickly. He is exaggerating of course, but it shows how angry he is at his mother's choice.

Hamlet is fairly angry from the very beginning of the play. There may have been a period between his father's death and his return to Elsinore when he was merely sad, but we don't see this. Hamlet's initial anger at both his mother and Claudius is driven by the fact that he returns home to find them married mere months after Old Hamlet's death. Whether or not the old king was murdered, Hamlet's angry reaction is first driven by his fury at his mother for marrying with such "wicked speed." He also feels that the marriage is "incestuous" and that Claudius is unworthy of his mother.
It isn't until after the Ghost asks Hamlet to "revenge his foul and most unnatural murder" that Hamlet begins to think there is something even more sinister behind the king's death and his mother's hasty remarriage. Prior to this, he agreed with his mother that his father's death had been "common" (that is, natural and usual), but he was very upset about it all the same.