Hypothesis: without Bismarck, Wilhelm I might abdicate in 1862, so his comparatively liberal son Friedrich reigns for 26 years (or even longer) instead of 99 days. His choice of Ministerpräsidenten closes the gap between conservative Prussia and the more liberal Southern kingdoms.
The Customs Union develops into a closer-knit confederation (->compare OTL 1868 Zollparlament) usurping matters formerly resolved by the "Deutsche Bund". Austria remains member of the latter, being curiously "one feet within, one feet without" a wondrous hybrid Germany.
By the time of Friedrich's death, Germany has continously transformed into a unified state with a Reichstag (equal universal male suffrage) in Frankfurt, a government headed by the Reichskanzler (elected by the Reichstag, confirmed by the Reichsrat), even less or no colonies.
Probably there will still have been a Danish war, so Schleswig-Holstein will be a sovereign member (not part of Prussia), Elsaß (-Lothringen?) depends a lot on butterflies, but would however not be under prolonged military occupation, but also a federal state within the union way earlier if annexed (-> in that situation my guess would be that German occupiers in case of a victorious war against France encourage Alsatians to secede who almost immediately join the German Confederation/Union as a member state).