You have qualified only Tier 1 of SSC CGL. It is a three-tier examination. So, you have not cleared SSC CGL till now. On the other hand, you have been finally selected for LDC in the State Government. So, I would advise you to join as LDC in the State Government. Immediately after joining, give a written intimation to the Administration (Establishment) Division of your new office about your candidature in the SSC CGL. In your application, you must state that in case of your final selection in SSC CGL, you will accept the job offer. Please keep a copy of your intimation after getting it duly acknowledged by the concerned officer.
If you follow the aforestated procedure, you will have no problem in tendering technical resignation in case of your selection in SSC CGL in future.
"If you are killed in action, you go to Heaven. If you win, you rule this Earth (as beautiful as Heaven). That is why, O son of Kunti, take a firm resolve and fight!"-- Shrimad Bhagwad Gita