What actually happened, probably, is that humans first counted by putting things in correspondence with fingers; actual bijections between fingers and things. This naturally led to ten, the number of fingers total and thus a grouping size of understandably frequent use, becoming a very significant number (culturally, linguistically, etc.). Ten was a very significant number for a very long time before positional notation with its digits and bases was invented. (The Romans had no digits, but they loved their fives and tens)

And thus, when such notation for numerals WAS invented, it felt quite natural to take ten as base, it being such a significant number.