You're applying for a job that never got posted

There's no vacancy, but there's a company you'd actually want to work for. This writes a speculative cover letter that opens with one specific, researched observation about their recent work, makes the case with two or three relevant things from your background, and closes with a low-pressure ask. Give it the role type, company and your background.

Write a speculative cover letter for {ROLE_TYPE} at {COMPANY}. There is no advertised vacancy. Structure it as follows:
1. Opening paragraph: one specific observation about {COMPANY}'s recent work or direction that shows genuine research
2. Middle paragraph: two or three skills or achievements from my background ({BACKGROUND_SUMMARY}) that are directly relevant to the kind of work they do
3. Closing paragraph: a low-pressure ask: suggest a brief call, not a formal interview
Keep the tone confident but not presumptuous. No mention of hoping or wondering.