Fresh-pressed grape juice is mentioned in the Talmud as acceptable to be used for sacramental purposes^(1).
It should be noted that ancient people didn't drink alcohol just to get drunk; fermented drinks (and foods) were often the safest to consume during a time without (reliable) refrigeration and pasteurization. There would not have been a good method to save large volumes of fresh, unfermented juice without it spoiling rather quickly other than turning it into some sort of alcohol. It should also be noted that "wine," at least in Roman antiquity, did not always mean what we refer to as "wine" now and could have a very low alcohol content (independent of it being commonly mixed with water). In Ancient Rome, drinking wine was a sign of being civilized, with water and milk being seen as lowly and barbaric^(2). However, there is evidence that Ancient Romans consumed some grape juice, usually referred to as "must." Virgil describes Roman women boiling down must to make a concentrated syrup, which wouldn't have been fermented and could be mixed with water to make a weak "wine"^(3).
I couldn't find much about apple juice, but there is evidence people in antiquity enjoyed pomegranate juice. Pomegranates enjoyed special prestige as a luxury, as well as value as a medicinal plant in the Ayurveda tradition and traditional Chinese medicine, with the juice especially being prized as a digestive tonic^(4).
Sources:
https://www.sefaria.org/Bava_Batra.97b.2?lang=bi&with=all&lang2=en
Broekaert, Wim. "Wine and other Beverages". The Routledge Handbook of Diet and Nutrition in the Roman World. London ;: Routledge, Taylor & Francis Group, 2019. Web.
Pope, Kyle. "The Ancient Process of Preserving Grape Juice".
Danko, Diana. "Pomegranates, from Antiquity to the present day". Alimentarium, 2015. Web.