The Russo-Japanese War escalating is one possibility as, while the Anglo-Japanese alliance was a mainly defensive one, the Dogger Bank Incident, precipitated by the Russian naval auxiliary
Kamchatka*, very nearly brought the British Empire into the conflict. The subsequent actions of the
Kamchatka only aggravated matters. Tensions remained high when the 1st Moroccan Crisis kicked off. With only a few small changes, such as Royal Navy vessels opening fire on the Russians and/or some diplomatic slips during negotians, both post Dogger Bank, during the Russo-Japanese peace talks and the Algeciras Conference of 1906, convened to settle the Crisis, these could easily result in an earlier WW1.
Alternatively, the 2nd Moroccan Crisis, aka the Agadir Crisis, very nearly started a war between the Anglo-French Entente and Germany in 1911. A third option would be the 1st & 2nd Balkan Wars, themselves triggered by the Italo-Turkish War, but those would only advance WW1 by a couple of years.
* Seriously, if you haven't heard of this ship before, or the actual voyage of the Russian Baltic Fleet to its ultimate fate, its one hell of story.