Tuhia he haere tonu mo tenei waahanga - I whanau a Bencic i Flawil i te raki-rawhiti o Switzerland ki a Dana raua ko Ivan Benčič. I whānau mai ōna mātua i Hīkosirovakia, engari i heke atu te whānau o tōna pāpā ki Huitene i te tau 1968 ki te rere i te whakaekenga a te Pakete o Warsaw.
e te Soviet Union. Ko tana papa he kaitakaro hockey ngaio i te Swiss National League A me te National League B i mua i tana noho hei kaihoko inihua. Ko tōna whaea he kaitākaro poitūkohu taumata-nui. I patu a Bencic i ana poipoi poipoi tuatahi i te rua o ona tau, ka tiimata te whakangungu me tana papa, he kaitakaro poipoi whakangahau hoki, mo te haora kotahi ia ra i te wha o ona tau. I uru ia ki tana whakataetae a motu tuatahi i taua tau, i hinga ia ki tetahi hoa whawhai e ono tau te pakeke ake i roto i nga huinga tuuturu me te kore e wikitoria i tetahi keemu. Ka aro tonu a Bencic ki nga hoa riri pakeke ake i a ia e tamariki ana, a i akiakihia e tona papa kia ngana ki te wikitoria i nga keemu e rua mo ia huinga.