ab urbe condita is definitely from the founding of the city (it usually meant ancient Rome) - urbe=city, as in urban, suburban etc. ab initio is the usual phrase.
Admittedly a pedantic observation, but ab origine means from the origin while ab initio means from the beginning or from the start. A small but perhaps significant difference, depending on the context in which each is used...
Gee, Octavius, isn't arguing against the sun (or the obvious) half of the fun of this site? Besides, from eggs to apples is another example of use in context, but doesn't really give the flavor (sorry) of an answer to the original question, do you think? Finally, bottoms up has to with ending, not beginning... again, rather pedantly...