I wonder whether there is any connections between the two letters. After all, they are both similar to the Phoenician Sade letter, and the Phoenicians were the dominant culture of the Mediterranean Sea for 1000 years, so that the letter had had more than enough time to travel to China.
The Chinese character 子 appears to derive from a drawing of a baby with arms spread, which has a corresponding word tsa in Sino-Tibetan, pronounced something like tsəʔ in Old Chinese. Greek zeta (Z), lower case ζ, derives from Phoenician zayin, and was phonetically [z]: presumably it derives from a picture of some thing that started with z, but the "thing" etymology is unclear. The origin of the letter Tsade (and other spellings) which was originally "emphatic" [sˁ] is also unclear, but its fate is that it gave rise to an ancient Greek letter San which disappeared from use. The first problem with your proposal is that it is believe that tsade is not related to zayin (but we can still consider it as a possibility, with the evidence being somewhat stacked against that idea).
The connection between Egyptian hieroglyphics and Semitic writing is also unclear, but it is credibly believed that Hieroglyphics at least influenced Semitic writing (e.g. ʕen looks like a picture of an eye). If we trace the Semitic letters back to the hieroglyphic shapes, any resemblance goes away, that is, the oldest shapes of the "child" character 子 looks very little like the "plant" shape thought to be the oldest form of Tsade, and also the "handcuff" picture thought to lead to Zayin. In other words, the comparison should not be between more modern shapes of letters, it should be between the oldest shapes. A comparison of Latin "w" and Hebrew "ש" would be completely misguided (the letters simply look similar), so your comparison correctly invokes sound-similarity as well as shape-similarity, but the older shapes are not sufficiently similar.