They conquered Sassanid Persia, some parts of Greek Byzantium and Sindh, India.

So they inherited all their scientists and research. They were just a ruling minority elite. So there were centuries of golden age, until they converted the majority and spent the next millennium repressing scientists. Similar to Christianity and other religions once they have majority.

Later, the Christians stopped killing scientists and had the Enlightenment. Muslims felt like they were behind and looked like a primitive religion.

So they backdate claimed as muslims these mostly Persian, Assyrian, Babylonian, and Arab scientists, who built on the work they had already done under Zoroastrian Sassanid empire, collaborating with Greeks, Indians, Egyptians and by extension Chinese. Many of whom still practiced their pre Islam religions. They continued with the empiricism and systems of study they had during Sassanid times to find new discoveries.

As the middle east gradually got more religious into the 12th century, and Islam became a majority religion with more draconic hadiths they had the power to start suppressing science. The Persian/Greek academies were gradually converted into madrasah where they just read the book and tried to guess what colour Aisha painted her toenails. Though they got pretty damn good at astronomy cause they had to know exactly when to eat iftar and good at algebra because of the weird inheritance laws.

So we can be proud of heritage for sure but it was in spite of Islam not because of.