You may qualify to adjust status with an Employment-Based Exemption under INA 245(k). But this exemption will not apply if you haven’t traveled since your last unlawful stay of more than 180 days. But you can travel on TPS AP and apply after 180 days and qualify for this exemption. Travel on AP comes with risks of being rejected entry since you were unlawfully present before.

This is not a legal advice. Consult an immigration attorney. These matters are much more complicated than they seem.

https://www.uscis.gov/policy-manual/volume-7-part-b-chapter-8