SW Visa Refusal Due To CoS Category

Hi.

I recently applied for SW visa and it was refused. The reason was due to missing defined CoS. Neither me and nor my sponsor (being first time sponsoring) knew the rules properly and i simply applied without Defined CoS. They tried to get everything sorted in time for defined CoS, but it got delay and i was refused the clearence.

Can i go into admin review in my case ? Would i be able to get decision in time ? Regarding admin review, i am in Germany on Blue Card Visa (eq. skilled worker), and i have already resigned for my current emplor to join UK job. So i have very short time to stay in german. Can i continue my admin review from home country ?