I don't really see it as China deliberately challenging Pax Americana.I am not rejecting China's accomplishments. What I am saying is that the West - especially Anglo-Saxon countries - still dominate the fields of technology, political discourse (including media), international trade and finance, and military. There is no point challenging Pax Americana as China still has lots of domestic issues to be dealt with, especially issues relating to its own domestic governance, political legitimacy, and relative technological vulnerabilities. When Germany went head-to-head against Pax Britannia in 1914, the German Army at least had marginally better rifles, artillery, and machineguns than the Brits. Although the Germany Navy was smaller, its dreadnaughts had more accurate guns, as demonstrated during the Battle of Jutland. German scientists turned out just as many state-of-the-art military technologies (like gas) as the Brits did. In fact, Germany was the first to field poison gas shells. If was only the entry of the United States that turned the tide of war against Germany. The sheer size of the combined British, Franch, and U.S. Navies also strangled Germany's maritime trade routes. Today, China has none of the advantages that Germany enjoyed prior to 1914.
China has spent a modest 2% of GDP on the military over the past 20 years, as per SIPRI.
In comparison, a militarised US and Russia averaged 4% over the past 10 years, which is twice as much.
So if China was really trying to challenge Pax Americana - Chinese military spending should be DOUBLE what it is today.
Plus this is off-topic, but you're looking at the wrong comparison for WW1 if you're looking at the military/economic balance.
The Dual Alliance (Imperial Germany + Austrian Empire) faced a larger Triple Entente (Russia + France + UK)
The Triple Entente had a population of 259M in total, which was over twice that of the Dual Alliance (119M)
And industrial potential which was 46% larger, as per Kennedy.
So Germany was always going to struggle to subdue its neighbours in Europe, never mind the impact the USA had.
In comparison, the China's economy and military spending is already larger than the rest of Asia.
Although China currently lags behind in technology level in many industries.
But in roughly 15 years, China should have a hi-tech economy roughly the same size as the rest of Asia + USA combined.
Plus Germany can be conquered in a single campaign as it is a small country.
It didn't have many natural resources and could be blockaded because it was surrounded by enemies.
In comparison, China is the same size as the continent-spanning USA which means it can be broadly self-sufficient.
Plus China shares land borders with lots of neutral or friendly countries, so it is difficult to blockade by sea.
China is also secure on land, as all of its neighbours know they can never hope to win a major land-war against China.
So China is free to focus on a naval conflict rather than on a land war
In comparison, German naval construction was slashed because the German Army faced a bigger enemy on its land borders.
In any case, China's goal is a peaceful UK-USA type power transition, rather than deliberately going to war.