One way to avoid general solicitation is to ensure that securities are only offered to those with whom the issuer has a “pre-existing, substantive relationship”.
Naturally, this raises the question: what is a “pre-existing” relationship? How long must the relationship have been in place? The clear answer here is that you must have known the other person before the securities offering began. (Brokers and investment advisors that have special rules.)
Similarly: what is a “substantive relationship”? This answer is a little more complicated, but the SEC provides guidance in its Compliance and Disclosure Interpretations (CDIs), specifically CDI 256.31 at this link.
An issuer must have enough information to evaluate if the buyer’s financial circumstances and sophistication is enough to make them an accredited investor or a sophisticated investor. That sounds like a pretty close relationship.