A recruiter can find you one opening. A relationship with a recruiter can help you see an entire organization, and who inside it might already know your name.
"Who is the account manager or person who oversees this client?"
Ask before you hang up. You may never need the answer, but if your recruiter goes quiet, you'll already know who else is accountable for that company relationship.
If you have a trusted staffing contact in your network, call them and explain your situation. Ask them to pull up Sales Navigator and walk the company roster with you.
One candidate had no idea a former manager of his had moved to the exact company he was targeting. It really can be a small world.
"If you were me, how would you approach this person?"
Don't just ask for an email address, ask for a strategy. A good recruiter can weigh in on:
Candidates often see it as a narrow transaction. Recruiters who know you well can offer far more.
That's exactly what happened for one QA engineer. While he waited on a slow response, I helped him find another path in. That path led to the interview.