According to the Royal Spanish Academy dictionary, the word tocar 'touch' has its origin in the toc toc onomatopoeia. Something similar is registered in Etymonline for the English verb touch:
from Old French tochier "to touch, hit, knock; mention, deal with" (11c., Modern French toucher), from Vulgar Latin *toccare "to knock, strike" as a bell (source also of Spanish tocar, Italian toccare), perhaps of imitative origin.
This source refers to a hypotetical verb toccare that existed in Vulgar Latin, that supposedly was the origin of our modern words. But I see that the word touch is translated into Classical Latin as palpo 'touch softly' (current Spanish: palpar) or tango 'touch' (origin of current Spanish tacto and tañer). So between these words and Old French tochier (11h century) or Spanish tocar (12th century) there must be a word that originated them.
So did the word toccare exist in Vulgar Latin as the origin of our current words for touch? If not, what could be transition from the Classical Latin words to the current ones?