He doesn’t take a moment to grieve his mother.
He doesn’t stop to say “Goodnight sweet mother” or any of it. He just goes right to villainy. With good reason, of course. There has, in fact, been some villainy afoot. Hamlet responds to the poisoning of his mother not her death.
Which is probably good. He can do more about the villainy than he can do about her death and he has not yet even taken in his own poisoning. It would be nice if there were a sort of St. Peter’s Gate because given how quickly these deaths follow on one another, mother and son would likely show up there at the same time. Also Laertes. And Claudius. It’d be a very crowded intake.