Griesbach's first bid for political office took place in the 1903 Edmonton election, when he made an unsuccessful bid for election to Edmonton Town Council, placing fourth of nine candidates in an election in which the top three were elected. He was more successful in the 1904 election when he was elected to a one-year term as an alderman to Edmonton's first city council placing eighth of seventeen candidates (in that first election as a city, Edmonton elected four aldermen to two year terms and four to one year terms, with the idea that four of the city's eight aldermen would be elected to two year terms each year). He was re-elected to a two-year term in 1905, finishing first of ten candidates.