You are right to identify the non-chronological approach that was taken in narrating this amazing tale. The first section is told in a flashback for example, which identifies the story is set in some kind of future dystopia where women sleep in a gymnasium that is surrounded by barbed wire and are not able to leave. This creates a feeling and mood of danger and fear that dominates the rest of the novel, which is set in the "present" of the future.
The way that the novel alternates between present and past and then is jettisoned into the future at the end of the novel in the "Historical Notes" section seems to create a feeling of instability and of fear, that precisely parallels the experience of Offred herself. The "Historical Notes" section at the end of the novel also allows readers to see the story of Offred in its wider historical perspective, giving us hope after a depressing and bleak narrative that such an era might not be the inevitable outcome of where we are heading but a minor blip as humankind works to improve itself and evolve towards greater sophistication and integrity.