First, we have no good evidence that Italian pasta has its roots in Chinese noodles. It's possible, since noodles have been made in China (and/or nearby, depending on exactly how you define "China") for 4000 years, but the earliest solid evidence for pasta in the eastern Mediterranean is in the 3rd-5th century AD.
Second, pasta/noodles travelled throughout most of Europe. We have Medieval pasta dishes from England, pasta was eaten in Spain, in France (including northern France, not just Mediterranean France), in Germany (where traditional types of pasta/noodles continue to be eaten today), Eastern Europe, and SE Europe. I'm not aware of any pre-modern pasta/noodles from Nordic Europe (Fennoscandia and Iceland) or Ireland, but they were known across the rest of Europe.
Given the wide range of pasta/noodles in Europe, we should ask why is Italy famous for them, and the rest of Europe not. The key is the types of wheat (and other grains) that were available. Durum wheat, which is the traditional type of wheat used for Italian pasta, is grown around the Mediterranean. Where durum wheat is grown, pasta (including non-Italian types, such as North African couscous) is common. Why? Notably, durum wheat is unsuitable for bread-making. In the "pasta belt", pasta competes with porridge. Outside the pasta belt, where common wheat (AKA bread wheat) is grown, pasta/noodles compete with bread and porridge. Given that pasta and bread both start with a dough made from flour and water, the major difference is in how they are cooked: boiling vs baking. Outside the pasta belt (in Europe, Western Asia, Central Asia, and South Asia), bread typically dominates pasta/noodles in importance. However, pasta (including filled pastas, like ravioli/dumplings) is typically known, and eaten.
Note that in Nordic Europe and Ireland, wheat is often a minor, or almost absent, crop, and rye and oats are the dominant cereals. This suggests that rye and oats are not well-suited for pasta-making.
For more on durum wheat, bread wheat, and pasta, see my past(a) answer in:
For more on the early history of pasta in general, see
I've encountered this story several times and I respectfully disagree with such claim.
Pasta as we understand it (at least in two of its forms, as elongated strips of different thickness and square sheets of dough) existed in the Italian peninsula well before the description Marco Polo gives of noodles when he travelled to China in the late XIII century.
What is nowdays and back then called vermicelli pasta (literally "little worms"), which described noodle-like pasta cooked by boiling it in water or chicken broth and served with grated hard cheese (the ancestor of Parmesan cheese). If the broth or water were not served, butter was added instead.
Already in the XII century, records mention of large productions of dry pasta in Sicily, mostly around the port cities in a similar fashion of what was happening simultaneously in Sardinia; it was seemingly a rather common provision that ships took aboard or traded with other Mediterranean ports like Pisa and Genoa and also Provence and even between southern Spain and North Africa during the XIII and XIV centuries. Also, in the second half of the 1200s, new eating utensils start appearing such as the fork, whose early spreading within the peninsula has been connected with the culinary staple of pasta, existing until the 1800s in the form of noodles or vermicelli alongside the lasagne (which most likely are an evolution of Roman laganae) and whose mentions start during the entirety of the XIII century.
More abundant informations regarding vermicelli do come from the late XIV and early XV centuries, but the current consensus is that the price control for wheat flour noodles and lasagna imposed in Palermo in 1371 and the description that one Florentine chronicler, Marchionne di Coppo Stefani, gives of the mass graves during the 1348 Black Plague as the preparation of lasagne with cheese, is a quite morbid metaphor portraying the preminence that this food had achieved alongside vermicelli, whose position as a food staple can be traced back already in the previous century also with another name, maccheroni.
Also, in the book about his travels to China, Marco Polo when describing the areas of the Orient, he never once mentions any sort of food resembling pasta if not in the case of a dish prepared in Sumatra using sago starch and used to prepare something he describes akin to lasagna and not noodles.
Sources:
Montanari, M. 2019, Gusti del medioevo. I prodotti, la cucina, la tavola, Laterza Editore, Bari;
Frugoni, C. 2021, Medioevo sul naso. Occhiali, bottoni e altre invenzioni medievali, Laterza Editore, Bari;
Camesasca, E., a cura di, 2003, Marco Polo. Il Milione, RCS Libri, Milano.