Per Merriam-Webster:

on the edge of (idiom)

: very close to (something)

Examples of on the edge of in a Sentence:

this film will have you on the edge of your seat from the first scene!
— Leah Hall, Country Living, 8 Mar. 2023

That block is on the edge of Denver and east of Peña Boulevard.
— Lauren Penington, Denver Post, 17 July 2025

If you are right on the edge of the tree line, I bet you can spot the cache container about 5 feet up!
— 2HikeNCache September 2025