This isn't very unusual or creative, but really go down every path you can to connect with someone who works there. It's the best way to get your resume past the initial gatekeepers.

Some ideas:
- Are you connected to anyone at the Startup on LinkedIn - invite them out to coffee

-Does any alumni from your college or High School work there reach out and introduce yourself

-Is anyone from the company speaking at any local events or meet ups go and introduce yourself.

Good luck!