I wouldn't say it was impossible, just quite unlikely. There were trends in Europe seemingly pointing to war becoming more unlikely as the years passed (or at least that it would become less likely once something that seemed very likely to happen sooner or later had happened).
There wouldn't be one POD to point to as responsible, though, more a set of events all going in the right way- but it is not entirely impossible that, from the first of January 1914, Europe avoids a major war. Not all crisises need lead to war, after all, as had been shown earlier in the century.