If the company wants to hire you now, they need to obtain an approved LMIA and then you will have to apply for a closed work permit. You can expect that it will take the company several months to obtain the approved LMIA (the employer will also have to pay a $1,000 processing fee).
If the employer doesn't want to go through the LMIA process, then they will have to wait until the Open Work Permit is approved. CIC is not going to expedite the OWP because you have found a job.