This is not legal or ethics advice: check your own state's rules, and ask ethics counsel when in doubt. Model Rule 7.3(b) bars live person-to-person solicitation (in person, live phone, real-time video) 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 that type of legal service for business purposes. That last exception does not cover every executive, and a company doing something for the first time may not qualify. California has no business-purposes exception, and Florida treats cold calls as prohibited solicitation.
So the default first touch is a truthful written message: a letter or an email, not a call, a DM or a chat. Written solicitations still fall under Rule 7.1 and Rule 7.3(c): no further solicitation once someone says they do not want to hear from you, and no coercion or harassment. Some states add more. Among other things, Florida requires "Advertisement" as the first word of an unsolicited email's subject line, a statement of qualifications that covers experience in the relevant area, submission to the Bar for review at least 20 days before first use unless exempt, and, when a specific occurrence prompted the message, a statement of how the lawyer learned of it. California requires the word "Advertisement" or words of similar import on written solicitations to someone known to need legal help in a particular matter, with narrow exceptions.
Run conflicts before any pitch, never pitch the other side of a deal your firm is on, and never pay for a recommendation beyond what Rule 7.2(b) allows. The limits travel with anyone acting for you: under Rules 5.3 and 8.4(a), a lawyer can answer for solicitation that BD staff, assistants or an agency carry out on the lawyer's behalf. The corporate clients guide covers these rules in more depth.