I think true science originated in post Catholic Europe/Britain, the befores were just froth and bubble; although the Chinese no doubt would claim they invented everything thousands of years before dinosaurs.
What year is that post Catholic Europe? If by true science you mean the modern scientific method of doing a literature review, propose a hypothesis, describe in detail the variables and methods to measure it and test the hypothesis... describe to the detail that it could be repeated by other scholars/scientists, then conclusion and suggested implication and further research etc... then it's relatively new - around 1850s?
But great sciences and its methods had been advanced long before this, in countries and cultures that is not Britain. There's the Greek philosophers and mathematicians who established the basis for rational thinking, the Arab astronomers, and yes, the Chinese philosophers, historians and generals who made conclusions based on observation s and not just hunches.
There's a saying that all philosophy after Socrates are just footnotes? Modern sciences are all micro steps, all incremental advances. That's not being dismissive of it. In my opinion, it's what made science "real science" and our world advances on that approach and we're eating and living (and killing) better because of it. BUT...
But I sense that you're a bit dismissive of the achievements of scientists and thinkers before this approach.
First, it didn't come about because the Western or British scientists are smarter and thought of it while others didn't. It came about because the Magna Carta eventually led to such thing as private property and intellectual properties and copyrights... with the law protecting private property, scientists and businesses start to trademark and publish their findings, thereby sharing it with the world - the world got a bit smarter, other inventors and scientists get to know what's out there and either go a bit better or put their effort elsewhere... that or wait until the copyright expires.
The Magna Carta and the rights of Man etc... that was only meant to be for free Men, and free Men then were only the Lords. Many happy accidents and a lot of self interests and here we are.
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With regards to China and their claims... I have never heard they ever claim to invent everything. They did consider themselves the Middle Kingdom, control all that is civilised under heaven while others are savages and barbarians... but they weren't the only ones with that kind of arrogance before or since.
Though they did invent paper money, bank cheques, printing, paper, gunpowder, fireworks, the compass, sailed their blue water naval fleet across Asia, India, the Middle East, Africa to project military might before an Emperor's death and near financial bankruptcy shut that down, leaving Columbus and Western countries to start their colonisation and become real powers.
If countries and people that so dominate and influence the world for so much of world's history could be laughed at and are either a basket case or a sick man only known for cheap knock offs; despite the wealth and undoubt creativity and intelligence, despite the great advances and our contributions to this modern world... perhaps history ought to tell us that we too could fall like all great powers has before us. I think it starts with establishing an empire then feeling invincible because of it.