If you are an L-1A visa holder, here are the steps you will need to take to obtain the EB-1C green card.
The first step is to have your employer file an I-140 petition on your behalf. Even for the EB-1C, you need a job offer in the U.S. in order to petition. However, as stated before, you do not need to have your employer obtain a PERM Labor Certification. Keep in mind that premium processing is not available for the EB-1C.
Once your I-140 has been received by the USCIS, that date will mark your priority date. You will need to check the visa bulletin released monthly by the Department of State in order to check if your priority date is current. Fortunately, the dates for the EB-1 tend to be current, meaning that you can file for an adjustment of status as soon as your petition is approved.
However, it is important to check the visa bulletin regularly to make sure that your priority date is current as there have been periods of time where a backlog has developed. In any case, when your date is current, you can adjust your status or go through consular processing to obtain legal permanent resident status.