Your double jump does not need to begin on a platform. Run or walk off a ledge and have faith.

This is the most difficult step. If you wait too long to jump after leaving the ledge, you will not be able to double jump.

Research is ongoing. Some trials indicate there is a window in which this 2nd jump must be performed before timing out.

Land at the GOAL. SHOW TIME!

Off-ledge double jumping allows you to cross greater gaps and take more direct paths. I do not believe it is possible to get "S" rank in Neo Osaka without it. Once I learned about this technique, the "S" ranks became more realistic, and a bunch of fun possibilities opened up overall.
Thank you, Siactro, for keeping the low-poly 90s alive and beautiful (•ө•) ♡