I notice you didn’t compare Rey with Anakin winning the podrace (no training), or with Luke using the Force to make a shot “that’s one in a million” (no training) as that would rather count against your Mary Sue argument.
Anakin was too perfect in TPM. I’ll agree with you on that, but he went through intensive training over the course of a decade between TPM and AOTC, and he got his share of challenges, and losses. He lost his mother, who was tortured to death, a fight against a Sith Lord, and his arm, and unlike Rey these things had enormous consequences for his development as a character.
Luke did recieve training aboard the Millenium Falcon, so I don’t see your point. You might argue it was not enough to make that shot, but it’s the difference between seeing Luke fail in using the Force and then succeed under the guidance of Obi-Wan. Luke was even guided by Obi-Wan when he made that shot. Rey had zero training or guidance by a Force user, none, and she still succeeded. That’s the difference.
Rather you go on about Luke having had a hard life - in fact Rey has had a far harder life than Luke. She raised herself as a scavenger and lived alone in a shanty. Luke had a relatively secure home life and upbringing. When Rey does finally make a connection to a Father figure that she has desperately wanted she sees him killed before her eyes… I’d say that qualifies.
Yes, that all happened in TFA, a film that I liked very much, and made me look forward to TLJ.