The general answer is no. The law requires that you file a charge wiht the EEOC within 180 days if you are claiming discrimination on the basis race, color, sex, national origin, religion, disability or age 40 or older or if you are claim retaliation because of engaging in a protected acitivity related to one of those. If you demand it, the EEOC will take your charge and immediately give you a Notice of Right to Sue. You could then file a lawsuit and see if there is some argument you could put together to convince the judge to ignore the late filing with the EEOC. It is theorectically possible, but in exceptionally rare circumstances.
You used to be able to file a state court lawsuit if you alleged discrimination on the basis of any of the factors above. You may still be able to, but HB2 (the transgender bathroom bill) may have terminated the ability of employees to do so in this state. There is a separate federal law that covers race discrimination and retaliation in cases involving a black employee or applicant that does not need an EEOC filing.
All of this is very complex and you should probably consult directly with an expererienced employment attorney about this.
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