Write a cold application to a company with no open role posted

You are writing a cold application email to a company that has not posted an open role matching what I do — this is a speculative outreach, not a response to a job listing, so it has to earn attention on its own.

PHASE 1 — IDENTIFY THE HOOK
From the company context below, identify one specific, plausible problem or gap this company likely has that matches what I can do. Do not invent a fact about the company you weren't given — if you're not confident in a specific problem, say so and ask me to confirm one rather than guessing at their internal challenges.

COMPANY CONTEXT
They just launched in a new country and their careers page has no listed operations or localization roles.

MY RELEVANT CAPABILITY
I ran market-entry localization for a similar-sized company's launch into three EU markets, cutting time-to-first-revenue by six weeks.

WHO I'M ADDRESSING THIS TO
Head of International Expansion — likely the actual decision-maker, not just HR.

PHASE 2 — DRAFT THE EMAIL
Open by naming the specific problem or gap, not by announcing that I'm job-hunting — the email should read like it's about their situation first. State my relevant capability as evidence I could help with that specific problem, using one concrete result rather than a list of skills. Explicitly acknowledge that I don't know whether they have budget or headcount for this right now, and frame the ask accordingly — not "are you hiring," but a smaller, answerable question like whether this is a problem worth a short conversation. Keep it to under 150 words in the body.

PHASE 3 — SUBJECT LINE
Write a subject line that names the specific problem or opportunity, not "Application for [Role]" or "Interested in opportunities at [Company]" — those read as mass-sent and get filtered accordingly.

WHAT NOT TO DO
Do not attach a resume-summary paragraph that lists job titles and years of experience — that's what the actual resume is for, not this email. Do not use "I've always admired your company's mission" or similarly unfalsifiable flattery. Do not ask them to "keep me in mind for future openings" as the primary ask — that's too passive to prompt a reply.

OUTPUT FORMAT
1. Subject line.
2. Email body, under 150 words.
3. A one-line flag if any part of the company context you were given felt too thin to build a credible hook from, so I can supply more before sending.