Start with a warm path: a partner who worked with the GC at a prior firm, a client who sits on the company's board, a banker the owner trusts. An introduction from someone the buyer knows is worth more than any note you write, and seeing who can introduce you shows where those paths exist. Let the introducer speak in their own words.
When there is no warm path, write. ABA Rule 7.3(b) bars live person-to-person solicitation when a significant motive is pecuniary gain, unless the person is a lawyer, has a family, close personal or prior business or professional relationship with you, or routinely uses the type of legal service you offer for business purposes. That exception does not cover every executive: an owner facing a first import or a first acquisition may never have hired that kind of lawyer.
California has no business-purposes exception, and Florida treats cold calls as prohibited solicitation. So skip cold calls, live video and DMs, and never ask staff or an agency to make contact you could not make yourself. Writing is the channel the Supreme Court protected: in Shapero v. Kentucky Bar Association (1988) it held that a state may not categorically ban truthful, nondeceptive letters to people known to face a particular legal problem. States can still regulate those letters, and many do.
A good note says who you are, names the business moment plainly and offers one general observation about the legal work that kind of moment usually brings. It avoids urgency, does not look like a legal notice, does not suggest you have already analyzed their legal problem, makes no comparative or results claims, makes no "certified" claim without a named certifying body, and includes your name and contact information. Florida adds "Advertisement" at the start of the subject line, a statement of your background, training and experience that covers the area of law involved, a disclosure of how you learned of a specific occurrence, and submission to the Bar for review at least 20 days before first use unless exempt. California requires an "Advertisement" marking in some cases. If the recipient says no, stop.