First off, 'modernize' is a bit broad. Let's take the question to refer to the railway programs in European Russia (specifically Poland), and the ongoing expansion of the Russian economy.

Mobilization

The generals of the First World War were highly concerned with timetables. The first to mobilize would also be the one to strike first, and also would gain time to prepare, if on the defensive. However, the Germans faced the problem of a war on two fronts after the signing of the Russo-French alliance. With the bulk of the Heer committed in France as per the Schlieffen Plan, the Germans initially relied on Russia's slow mobilization and primitive logistics and infrastructure to slow down an assault on East Prussia until a decision was reached in France.

The Railways

The French were aware of Russian backwardness, and a series of French loans with the condition that the Russians develop a rail net in Poland helped the situation. Additional Russian funds were allocated to infrastructure in any case, and for a connection to Siberia and the Urals, the Trans-Siberian had been (mostly) completed by 1914. This, together with the Russian General Staff keeping a 'pre-mobilization' force in Russian Poland and placing the western districts on 'mobilization alert' before announcing a full mobilization, meant that within a couple of weeks after declaring war and anouncing said mobilization, the Russians could field a substantial army to threaten East Prussia.

Economics

Towards the end of the 19th century, Germany was one of the biggest economies in the world, and was still growing. However, Russia was growing faster. Between 1860 and 1913, Russian industrial output grew at 5% p.a., and from 1890 to 1914, coal output rose sixfold. By 1914, Russia was also the world's sixth-largest trading nation, and had laid more than 10000 miles of rail track from 1900 to 1914. Granted, this left Russia far behind Germany, the U.S., and the British Empire, but the steady growth, coupled with Russia's sheer size, overawed many observers (the younger Moltke included).

Finally

Thus, we see that the Tsar's empire was not 'invincible', but given time could probably outweigh Germany. By 1914, it was already upsetting Schlieffen's careful timetabling, and threatening East Prussia with close to half a million men much earlier than expected.

Sources-

1. Paul Kennedy, The Rise and Fall of the Great Powers

2. Norman Stone The Eastern Front:1914-1917

3. John Keegan The First World War