In general, if you are going to be using magic or any non-scientific element, you need to introduce that very early in the first half of the first act, probably in the first pages of your story.
The first Book of Harry Potter, for example, shows magical fantasy elements starting on page 3 -- A man sees a cat reading a map under a lamp post, if I recall. Then several other such elements.
The first half of the first act establishes your protagonist's "normal world". About an eighth of the full story is devoted to this, and at the end of this eighth, we first see the "inciting incident" of the story, which in the next eighth will grow to force the protagonist out of their normal world; doing something or going somewhere they never would have gone without the inciting incident becoming disruptive of their normal life.
Your "contract" is established in that first eighth; if magic is a real thing you need at least ONE strong hint of it early, while the reader is still accepting anything. Time travel, FTL spaceships, robots, super AI, Magic, sorcery, shape-shifters, Aliens, vampires, werewolves, fairies, elves, whatever. All of those have made good stories, because when we begin to read, we are ready to accept anything you want to give us.
But your credit runs out fast! If you introduce magic too late, it looks like a deus ex machina to solve some writing problem. You have to write the final 7/8ths of the book with what you introduced in the first 1/8th.
Now, "magic" is what is introduced in the first pages of Harry Potter, but obviously nowhere NEAR all the magical things that will be done. More spells, and more powerful magic is introduced throughout. That's fine. Once you introduce "X", more and bigger variants of "X" are fine. You only need to introduce one extraterrestrial, once you have done that you can introduce thirty more species and the audience is not surprised or disbelieving. Extraterrestrials exist.
So the task isn't impossible, you just introduce a category of not-real-world something, and that opens the door to everything in that category. But they are categories: "Magic" doesn't permit "Extraterrestrials" and vice-versa, many would say neither allows "ghosts", or "time travel".
It is also possible the "inciting incident" is itself in the category of your fantasy or SciFi element. For example, the protagonist discovers something magical. That can be the signal to the reader, too.
EDIT in response to OP's revision and request.
I think 8 chapters and 25% of the story is far too late to introduce magic. I base that on the Three Act Structure, which was derived from a fair generalization of thousands of successful stories and how they are structured.
The magic you introduce doesn't have to be by the MC, it could be something observed by a stranger. It doesn't have to be any kind of "big magic", but it does have to be there. As I said, your credit runs out fast!
If you need to rewrite, you need to rewrite. Don't fall for the "sunk cost" fallacy, a story that doesn't work needs to be fixed. Your characters can blow off the magic as something they just didn't understand, this doesn't have to change the progression of their actions; but you need some event with some walk-on character that is unambiguously (to the reader) magic.