Anthony, it is beneficial to have (good) credit, however, that isn't always possible for first time applicants or women who are recently divorced and without a work history. Property management companies usually have stricter guidelines than properties managed by individuals.
A Lease Guaranty (TX), which ensures payment by another individual, such as parents or ex-spouses, may be considered, along with any form of good credit and/or rental history. Additionally, prepare a letter of explanation regarding the circumstances. However, it is totally up to the discretion to the person reviewing the application.