Chinese uses no prepositions for dates and times.
Japanese uses the particle "ni" for specific points in time. (It's the same particle that means, "in," "at," and "to" in other contexts). You use it in phrases like "I'm leaving AT 8:00" or "I was born ON June 1st" or "He died IN 1980." But you wouldn't use any particle to say things like "tomorrow," "today," "this year," etc.
So there's your input from some non Indo-European languages.