Animals don't start out full sized.

Wiki on the Eagle Owl's diet

Though not often, Eurasian eagle owls occasionally kill the young of ungulates, mainly roe deer (Capreolus capreolus) fawns. The size of roe deer fawns taken by eagle owls can vary, from 1,500 g (3.3 lb) to 13,000 g (29 lb) in weight. Small adult-sized roe deer, weighing up to 17,000 g (37 lb) have been recorded as prey, though these specimens have possibly previously been injured or taken as carrion. Eagle-owls also take wild boar (Sus scrofa) piglets and young reindeers (Rangifer tarandus) as prey and possibly pose a threat to young of ibex (Capra ibex) and red deer (Cervus elaphus). They rarely hunt domestic ungulates, though predation on “half-grown”domestic sheep (Ovis aries) has been reported.