When did “word” become a synonym of “promise” for the first time?
This a question for historical linguistics, and such questions are usually unanswerable because the ideas of a language might actually predate a language itself and languages themselves don't, strictly speaking, have beginnings and ends. If Modern English has the expression, "to give one's word", then it seems Middle and Old English do too, which then begs the question is it proto-Germanic? For instance, if a speaker of the Bokmål, uses the same construction to communicate the same meaning, then likely there has never been English where 'to give a word' was never used, and that's because there is not strict dividing line between proto-Germanic, Frisian, Old English, Middle English, etc. In fact, dialects of languages are difficult to define as dialects in opposition to distinct languages, a fact that Scots and Veneto speakers might realize given their often contested statuses as distinct languages. The fact that OED has examples going back to old English doesn't necessarily mean that the idiom began there. It may very well go back to the Romans, in which case on Latin Stack Exchange, you might be able to ask the same question and date the idiom back to the beginning of Latin. And even then, who is to say that it wasn't used well before its first known archaeological appearance? The idiom may have been used by the putative speakers of PIE.