Would you like some noodles is the correct one!

In all practilaity, you could say either. No native speaker would really notice the difference in normal speech. I would argue that we could have a change depending on the context: If you expect the person to say yes. For example, you are the dinner table and the noodles are right there ... you would say some. If you are not sure or you expect the person to say no ... you would say any.

First off, both are gramatically correct. The choice of either one depends solely on context. So for the first one, imagine going to a McDonald's (if McDonald's had noodles on the menu) and ordering a salad, the cashier might ask you "would you like some noodles with that?" this implies there's only one variety of noodles just like "would you like some fries with that?" implies there's only one variety of fries. The same example, but imagine a vast amount of different noodle varieties to choose from, the cashier would ask you "would you like any noodles with that?" pointing to the menu where all the different noodle types are listed, there's a "variety of" implied in that question as in "would you like any (variety of) noodles with that?". Now, in these examples "some" can be used in both, but "any" would be awkward (unnatural) in the first one.

IMO both is right... Looking forward too!!