What can I do if I was wrongfully accused of theft at a workplace and immediately fired with no investigation or evidence?

This may not make you feel much better. But employers do not have to investigate theft. They do not have to be right. They can and often do tell employees lies. The reason most employers conduct investigations is to have some evidence that they did not discriminate. When employees file discrimination charges that often does cost employers lots of money win or lose. Then defense lawyers earn their money because they end up doing the investigation that was never done. You gave no facts of discrimination nor hostile work environment nor anything else that may have been illegal. If you have such evidence you can file with the EEOC for up to 300 days or with New York State's Division of Human Rights. They both do good work. But unless an employment lawyer helps you it may not result in a financial recovery for you. And most of us stay busy and we have to select the best claims because we too have to earn a living. Good luck and thanks for asking. Fairness is generally not written. We just do our best to make it happen if the facts are strong and the law is on our side.