It is absolutely legally possible to apply for a green card from TPS (provided you were not out of status before you were on TPS). Show this to your employer:
https://www.uscis.gov/humanitarian/temporary-protected-status
"TPS is a temporary benefit that does not lead to lawful permanent resident status or give any other immigration status. However, registration for TPS does not prevent you from:
- Applying for nonimmigrant status
- Filing for adjustment of status based on an immigrant petition
- Applying for any other immigration benefit or protection for which you may be eligible
PLEASE NOTE: To be granted any other immigration benefit you must still meet all the eligibility requirements for that particular benefit. An application for TPS does not affect an application for asylum or any other immigration benefit and vice versa. Denial of an application for asylum or any other immigration benefit does not affect your ability to register for TPS, although the grounds of denial of that application may also lead to denial of TPS."
