I am not aware of any nonprofit corporate law that imposes a specific minimum length of time as a member before a person could vote or run for office.  It would be highly impractical for a newly formed corporation if no one is eligible to vote or hold office until six months or a year after the corporation was formed.  It might be a little difficult to engineer the start-up without accepted leadership.

Some membership organizations impose experience requirements for officers after the organizations have been around for a while and the old timers decide they have experience and interests that newbies cannot possibly possess or might try to undermine.  You will see this more frequently in older community associations or social clubs.

I have never seen a situation in which a time delay for voting was imposed on anyone who was actually a member on the record date for determination of who has the right to vote.  In fact, the very legal definition of “member” in many state nonprofit corporation laws is based on whether the person has the right to vote on organizational matters.

If you really want to delay the right of new members to vote, it would be better to admit them first as junior, associate, probationary, (or some other title that means “not really”) members, who don’t get full rights of membership until after the passage of time and perhaps a second approval.  That would be much more likely to be considered legitimate than trying to deny voting rights to actual members.