Can I legally work with a valid I-94 (Ukraine Humanitarian parolee) and Social security number marked as not eligible for employment ?

As a Ukraine humanitarian parolee, the parolee status allows you to remain in the US, but unfortunately does not allow you to work. You will have to wait until you receive the EAD. I note that USCIS will expedite an employment authorization request for among other reasons severe financial loss to a company or person, provided that the need for urgent action is not the result of the petitioner’s or applicant’s failure: (1) to timely file the benefit request; or (2) to timely respond to any requests for additional evidence; and for emergencies and urgent humanitarian reasons. You can generally request expedited processing by calling the USCIS Contact Center at 800-375-5283 (TTY 800-767-1833) or by asking Emma after you have obtained a receipt notice.  (You can access Emma by typing "Ask Emma" on the internet). The USCIS Contact Center will not be able to refer the expedite request to the appropriate office without a receipt number. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence