I took an experimental class in high school which taught topology and knot theory to people with a pre-calculus background. We used an early draft of a textbook (not sure of the title or if it’s even been released - our teacher got access because she knew the author) and a lovely knots textbook called “The Knot Book.”

I think we gained a really good intuitive understanding of homeomorphism, neighborhoods, and homology groups. Knowing about these topics has been super useful in my studies and career.

On the other hand, some of the algebraic components of topology went totally over my head. So I do think there’s a limit to how much you can understand without diving into other fields.

Also, we had the benefit of a trusty excellent mathematician as our teacher, which helped quite a bit. Good luck diving into this field, I hope you find it rewarding!