German leadership was the decisive external factor emboldening Austria-Hungary to declare war on Serbia in July 1914.
Kaiser Wilhelm II and Chancellor Bethmann Hollweg promised unconditional support for any Austrian action against Serbia, even at risk of world war. This removed Vienna's fear of isolation.
German Foreign Minister Jagow and Ambassador Tschirschky urged a harsh, short-fused ultimatum designed to be rejected, providing a pretext for war. They discouraged delay.
When Britain proposed a 4-power conference (July 26), Germany rejected it. When Russia urged restraint, Germany feigned ignorance while accelerating its own mobilization plans (Schlieffen Plan).
Germany demanded Russia halt mobilization; when it refused, Germany declared war (Aug 1), transforming a Balkan crisis into a continental war.
Berlin calculated a localized Austro-Serbian war was impossible; they preferred a general war now (before Russian military reforms completed ~1917) over a delayed confrontation. The "blank cheque" was the license Austria needed to pull the trigger.