The narrative effect of telling a story in an interesting way will make the story more interesting.
Reasons to tell this particular story out of order:
The whole story intends to focus on two major things: The child's development of mental illness, and how his mother dealt with that.
The 'climax' does not conveniently occur at the end of the chronology.
In typical 3-Act structure, your story might be re-ordered to begin with the family dynamic as the central conflict. The child being surrendered to an institution (or whatever) could be the mid-story low point, indicating they cannot continue with the status quo. The emotional climax is the acknowledgement of the death itself which occurred much earlier. Finally addressed, this will lead to a long recovery/resolution.
The catalyst is a mystery.
We know something has happened to disrupt this family, but we don't know exactly what. We see the signs of dysfunction, grief, and coping. The story is focused on these character dynamics, not the events that triggered it. The tragedy serves as a kind of MacGuffin for the reader, they will search for clues once they become aware of it.
Knowing the chronology would bias the reader.
We need to develop sympathy for the boy before we understand that he is the root cause. We also need to see the mother lashing out/falling apart at seemingly irrational and unreasonable moments, making her unsympathetic before we learn her tragic predicament.
Which came first: Chicken or Egg?
Focusing on the family's dynamic, without knowing there are specifc circumstances leading up to it, creates a chicken or egg effect in which we might assume the mother is the one with the mental illness, and her inconsistent behavior towards the son is causing his problems. The reversal of these assumptions is a plot twist that creates story 'depth' once their behavior is re-framed by the truth.
The son's mental condition is meta to the reader's experience
The story is fractured, deliberately obfuscating the cause and effect of the events. This mirrors the boy's internal state and his sense-of-self which is eroding. The reader must piece together what really happened, despite an unreliable narrator.
What is real?
The son could talk about his brother in the present tense, a brother we never see. Is he imaginary, maybe a coping mechanism against the family's abuse? The mother's reaction towards this 'imaginary' brother might be inexplicably hostile or triggering. By stages we learn there is a brother, he has died tragically, and the son killed him.
The linear story has a too obvious conclusion
By withholding the details of the tragedy, readers are not able to jump to the obvious: this family needs professional help. Through grief and dysfunction they will each make bad character choices which compound their problems. Readers may be frustrated when the solution is inevitable but characters are actively sabotaging getting there.
Social Worker as detective
It's a trope, but a limited 3rd-person POV from outside the family could experience their own investigation chronologically, while unraveling the 'mystery' in a non-linear way. They might be a psychologist, a court-appointed case worker, or a family friend. The events could be known, as well as the aftermath. The 'mystery' is why, or even potentially that the death was not entirely an accident.
A Hobson's Choice isn't really a choice
The story might center on the mother who is faced with a Hobson's choice of protecting her remaining son, and justice for her dead son. Under the pressure of an unresolvable inner conflict, she might obscure the truth or implicate herself.