In Hamlet, Hamlet's tragedy is that he is, at an advanced age, still an adolescent who is just facing the reaity of evil and duplicity in the world for the first time. I need two supporting points.
The excellent movie The Graduate (1967), which starred Dustin Hoffman when he was still quite young, seems to be a modern spinoff of Shakespeare's Hamlet. Hamlet has buried himself in school at Wittenberg and still wants to go back there for more studies. It seems very true that he is facing the reality and duplicity of the world for the first time, even though I believe the dialogue establishes somewhere that he is nearly thirty years old. I suspect Shakespeare had to establish that he was around thirty because the actor who played him was obviously not a youth. Otherwise, Shakespeare might have made the character only around twenty, which would have been more appropriate. When Laurence Olivier played Hamlet in his film version, he looked a lot older than thirty. His film was released in 1948 and he was born in 1907. So he was forty years old when he made the production--and he looks it!
Hamlet's age is established in a roundabout way in the scene with the gravedigger (5.1.130ff). The gravedigger says, "I have been sexton here, man and boy, thirty years." He says he started on the "day that our last king Hamlet overcame Fortinbras," which "was the very day that young Hamlet was born." Shakespeare takes pains to establish Hamlet's age precisely for some reason.
If Shakespeare's Hamlet was thirty, then one would expect his mother to be close to fifty, which is pretty old for the way she is behaving with Claudius. I think the Hamlet character must have been much younger in the first draft of the play and that Shakespeare had to make him older because he was going to cast an older actor in the part. It might be argued that Hamlet is not really a thirty-year-old acting like an adolescent, but a real adolesceent who got rather awkwardly transformed into a thirty-year-old by the playwright. In the movie The Graduate, the hero would be about twenty-two, which is the average age of college graduates. Hamlet should be about twenty-two himself.
King Lear is also about a man who is just understanding the "evil and duplicity of the world," yet Lear is an old man. In his case, he was regularly and systematically fooled by people because he was a prince and then the king. It wasn't until he gave up his crown and all the power that went with it that people, including two of his daughters, began to show him their true faces. There are similarities in works like Don Quixote, Timon of Athens, The Prince and the Pauper, and Huckleberry Finn. Also in The Catcher in the Rye. Also in Candide, and probably a great many others.
I love this question! I do think it is a perfectly valid view of Hamlet to consider him in this way. There is something of the teenager in his temper tantrums, depression and mood swings that could be used to suggest he is actually a maladjusted teenager who is finding it so very difficult to adapt to what is going on around him.
Let us first of all consider his mood and depression in Act I scene 2. Even though we know that his father has died recently and his mother has remarried so quickly after, there is something rather extreme in his insistent mourning that does make us sympathise with Gertrude when she says to her son:
Good Hamlet, cast thy nighted colour off,
And let thine eye look like a friend on Denmark.
Do not for ever with thy vailed lids
Seek for thy noble father in the dust:
Thou know'st 'tis common; all that lives must die,
Passing through nature to eternity.
The way he is obviously still wearing mourning black in spite of the joyful occasion of his mother's wedding and her happiness hints at an obsessional grief and fascination with his father's death that indicates an inability to accept his death.
Secondly, you might like to consider the extreme way in which Hamlet reacts to the various discoveries of betrayal and deception around him. Consider his rage at Ophelia in Act III scene 1, which some productions suggest is when he realises that Ophelia has been set up to find out what is wrong with him. When even his lover turns against him, he literally loses it:
Get thee to a nunnery: why wouldst thou be a
breeder of sinners? I am myself indifferent honest;
but yet I could accuse me of such things that it
were better my mother had not borne me: I am very
proud, revengeful, ambitious, with more offences at
my beck than I have thoughts to put them in,
imagination to give them shape, or time to act them
Brannagh's production in particular has Hamlet shouting these words at Ophelia whilst trying to locate her father and Claudius. Such extreme reaction again smacks of hyperbole. We are presented once again with a character who just is not able to process what is going on around him.