In many of the pesukim being discussed, the actual reference is the Egyptian city of Pelusium. Or to some other Egyptian city. (Targum Yonatan translates "Raamses" as Pelusium, after all.)
Thus, e.g., in Yechezkel 30:
, Sin is called the "stronghold of Egypt." And indeed the other place names - No and Noph - are also places in Egypt. See Metzudat David on the pasuk, where he calls it the city of "Sin," meaning that it is a city in Egypt.
Of course, in modern Hebrew, it means China. And in English, we have the word "Sinophile." Sino as referring to China has the following etymology, to cite the American Heritage Dictionary:
[From Late Latin Sīnae, the Chinese, from Greek Sīnai, from Arabic Sīn, China, probably from Chinese Qín, Qin; see Qin.]Of course, that does not mean that it must have meant the same thing in ancient Hebrew.
However, perhaps we can find such reference to "Sin" as China, in a Biblical source. Specifically, we will look to Yeshaya 49:12:
|יב הִנֵּה-אֵלֶּה, מֵרָחוֹק יָבֹאוּ; וְהִנֵּה-אֵלֶּה מִצָּפוֹן וּמִיָּם, וְאֵלֶּה מֵאֶרֶץ סִינִים.||12 Behold, these shall come from far; and, lo, these from the north and from the west, and these from the land of Sinim.|
We see eretz Sinim as contrasted with tzafon and yam, which are North and West. It might make sense to say that it contrasts with yam, such that it is a land in the East. In which case, in this pasuk (only), it refers to as eastern country, which perhaps might be China.
However, there are three other possibilities -- contrast it with North to get South; make it identical with the general Biblical Sin, which is the city in Egypt; or make it the land of the Sinites, who are descended from Canaan, as we see in Bereishit 10.
As we see, Targum, either via tradition or logic, decides that it means ארע דרומא, a Southern land. And Jastrow in his dictionary (page 983) also says that eretz Sinim is a homiletical name for the South.
This is something known to the Amoraim of Eretz Yisrael, for it occurs in Bereshit Rabba 52:4:
Thus, it is a synonym for "South."ויסע משם אברהם פנה מפני ריח רע, שהיו אומרים לוט בן אחי אברהם, בא על שתי בנותיו.
ארצה הנגב, שבעה שמות נקראו לו:
דרום, נגב, תימן, ים, וימין, וסנינים. [נ"א וסינים]
היתיבון, והכתיב: (תהלים פה) ולא ממדבר הרים?!
אמר להם: אף הוא, דרום הוא.
Rashi also takes this translation as "Southern land." As does Metzudat David.
Another possibility, as we mentioned, is that it refers to those descendants of Canaan. We see in Bereishit 10:
Indeed, this is what Metzudat Tzion says, that it was named after its residents, and gives reference to Bereishit 10.
Radak combines the above two ideas. That is, it means the South, like Targum Yonatan. But that is because the Sinites, mentioned in Bereshit 10, lived in the South.
Ibn Ezra, meanwhile, connects it with Egypt, saying it is at the edge of Egypt.
Based on the explanations here, in "Adam Clarke's commentary," we see that "Prof. Doederlein thought of Syene, the southern limit of Egypt," and another possibility is a woodland.
Meanwhile, Strong's Concordance states that "Sinim is a distant Oriental region." And Young's Concordance writes "Sinim is a people in the far east; the Chinese?" If so, we have claims that it means the east and thus that it could mean China.
Thus, it is possible that this is a reference to China in Yeshaya, but not if we hold by the translations offfered by the classic Jewish commentaries.