Kammala jumla mai zuwa: An haifi Bencic a Flawil a arewa maso gabashin Switzerland zuwa Dana da Ivan Benčič. Iyayenta duka an haife su ne a Czechoslovakia, amma dangin mahaifinta sun yi hijira zuwa Switzerland a 1968 don tserewa daga
Tarayyar Soviet ta mamaye yarjejeniyar Warsaw. Mahaifinta ya kasance ƙwararren ɗan wasan hockey a cikin Swiss National League A da National League B kafin ya zama dillalin inshora. Mahaifiyarta ta kasance babbar 'yar wasan kwallon hannu. Bencic ta buga wasan kwallon tennis na farko a lokacin da take da shekaru biyu kuma ta fara horo tare da mahaifinta, wanda shi ma dan wasan wasan tennis ne na nishaɗi, na awa daya a kowace rana yana da shekaru hudu. Ta shiga gasar ta farko ta kasa a wannan shekarun, ta rasa abokin hamayyarta mai shekaru shida a madaidaiciya ba tare da lashe wasa ba. Bencic zai fuskanci abokan adawar da suka fi girma a matsayin yaro kuma mahaifinta ya karfafa ta don kokarin lashe wasanni biyu a kowane tsari.