Probably from Scandinavian, related to 'get' — guessing was 'getting at' an answer without full knowledge.
To estimate something without sufficient information.
Probably from Scandinavian, related to Old Norse 'geta' (to get, guess), from Proto-Germanic *getaną (to obtain). You 'get at' the answer by trying. Key roots: *getaną (Proto-Germanic: "to obtain").
'Guess' and 'get' may share the same root — both involve reaching for something.