Default to a written first touch: an email or letter from the lawyer who would do the work. It gives the reader time to think, and the ABA's comment to Rule 7.3 names mail and email as the alternative to live contact.
Keep it short: say who you are and what your practice does. Name the moment plainly and, where your state requires it, say how you learned of it. Offer one useful thing with no strings, such as a short briefing. Close with your name, firm and contact details, and make it easy to say no. Before it goes out, check your state's rules: some require an 'Advertisement' label, a statement of your qualifications or Bar review first.
Never imply you have reviewed their documents or spotted a problem ('your new lease exposes you to...'). You have not, and you cannot back it up. Skip urgent or official-looking subject lines, suggestions they must act, specialist claims without a named approved certifying body, comparisons with other firms and promised results. Never name other clients or matters without consent.
Example (invented): after conflicts clear and the state's advertising rules are checked, a partner writes to the general counsel of a 150-person HVAC services company that has agreed to buy a smaller competitor in the next state. The note says the firm handles post-closing employment, lease and supplier-contract work for building-services companies, and offers a two-page general overview. It ends by saying there will be no follow-up if the GC is not interested.