Is it possible to have blocked arteries at the age of 23?

Yes. Although rare, it can happen. Some of the possible causes are buerger's disease (blockage of small arteries related to smoking), vasculitis, severe raynauds disease (vasospasm from cold exposure), collagen vascular disease, embolism, popliteal entrapment or popliteal adventitial cystic disease.
Yes. Vessels can be blocked by trauma or congenital problems like popliteal artery entrapment or thoracic outlet syndrome. Pad is rare in this age group. Juvenile diabetics are at increased risk.