State laws differ on the default provision for membership in nonprofit corporations if nothing is stated in the articles of incorporation.  In some states, you can have members (who are analogous to shareholders of a business corporation) if you don’t say otherwise.  In some states you can’t have members unless you say you will in the articles.  (Founders should check with a lawyer who understands the applicable state law if they have a question on this.)

Since you say your structure is definitely a non-member corporation, you will have to amend your articles of incorporation to permit membership. That is a technical action that will have to be filed with the state as an amendment to the articles (for which there is probably a form on your state website), but is not particularly difficult. For those who have named a board and commenced operations, you will need the approval of the directors to amend the articles. (For founders thinking of changing after several years of operation of their organization, it may not be possible to get the approval of directors who already have full power.)  In any case, you will have to amend your bylaws (See the Ready Reference Page above) to provide the protection you want.

You ask about the founder serving as the “Director” of the organization while also serving as the sole member.  If you are asking whether the founder can be a member of the board of directors, the answer is clearly yes.  If you are asking whether the founder can be the “executive director” or CEO of the corporation, the answer is also clearly yes.  Whether the founder (or anyone else) can be both the paid CEO and the chair of the board of directors is a matter of state law, and a few states have apparently prohibited that.  But even that limitation should not be an insurmountable burden for the founder who wants to retain the ultimate control of the corporation.