Urgent:
1) Go to SSA office tomorrow (while 2 year GC is valid), file form SS-5 for replacement SS card without restrictions on it. The restrictions is wording "Valid for work only with DHS authorization". You'll have to show GC and ID to SSA personnel. If you don't have restrictions on your SS card, see the step 3.
2) In few weeks you will receive unrestricted SS card.
3) Assuming you have state ID or DL card that's valid, all you need to show employer is valid DL and unrestricted social security card for I-9 verification.
Employer by law cannot demand to see your GC. List B and list C documents are enough to verify your work eligibility.
List B document in your case is state ID or DL. List C document is unrestricted SS card.
More info: https://www.uscis.gov/i-9-central/form-i-9-acceptable-documents
Do not ever use GC for anything other than:
1) travelling into the US (airlines, CBP)
2) getting new / replacing ID / DL at DMV / BMV / DSP or whatever agency issues DL in your state
3) Banks when getting a mortgage / loan etc.
This will save you a lot of stress.
Good luck!