Here is a great step by step: (1) How to start UiPath Job through API | LinkedIn
I suggest following the suggestion to make it work in Postman first so you know you have all the data figured out before implementing that in your remote application.
Another way to look at that is: can the application write a queue item in Orchestrator (via API)? You could start the automation from that trigger as well. Same for email triggers (have the app send an e-mail with specific content that you can use to trigger your automation).
Hopefully this helps!
Thx,
CV