Putting Highest Degrees First Act of 2023 or the PHDs First Act This bill exempts certain non-U.S. nationals ( aliens under federal law) with doctoral degrees from direct limitations on the number of immigrant visas granted per year. The bill also allows an individual to get a student visa for a doctoral program even if the individual intends to seek lawful permanent resident status (also known as a green card ). To be exempt from the numerical limitations, the individual must (1) have earned a doctoral degree (or the highest degree available if a doctoral degree or its equivalent is not available in that field) while in the United States attending an accredited higher education institution, (2) be employed (or have a job offer) in a field related to the degree and earn at least the median wage for that occupation, and (3) meet certain labor certification requirements. The bill also allows an individual seeking a nonimmigrant F-1 (student) visa to obtain a doctoral degree to have dual intent. Specifically, such an individual may obtain the nonimmigrant visa or change nonimmigrant status even if the individual intends to apply for a green card. (Generally, such an individual may be denied the nonimmigrant visa unless dual intent is allowed for that type of visa.)