There isn't really direct evidence to my knowledge, but it is becoming increasingly apparent to the academic community that this would have been the case. There exists a long history of trade across the periphery of the Indian Ocean that at the very least goes back to 3000BCE, if not much earlier in history than that. I personally would direct trade contact to be unlikely, although it certainly could have happened through intermediaries.

There was definitely potential for Chinese goods to reach the Kingdoms of Israel and Judah, although I'm unsure in what numbers they actually would have done so. They would probably have arrived through several geographicnintermediaries, such as India, and Mesopotamia or Egypt, before arriving in the eastern Levant.

Also note that these states (and maybe the united monarchy, if it existed) emerged as polities during the Bronze Age Collapse, so it is likely that there was a lot of chaos around trade routes at the time due to global environmental changes, which might diminish the possibility that these kingdoms had extensive trade ties.

This is unrelated to a question on China, but India is actually mentioned a small number of times in the Torah, and has a much better track record of being potentially known of by people after the creation of the Kingdoms. The Indian subcontinent had a particularly prolific trade with Mesopotamia and Egypt during that time period, and would have been known of by those in the right circles.

Sun, W.- et al. Origin of the mysterious Yin-Shang bronzes in China indicated by lead isotopes. Sci. Rep. 6, 23304; doi: 10.1038/srep23304 (2016).

Pollard;Rosenberg;Tignor, Elizabeth;Clifford;Robert (2011). Worlds Together Worlds Apart. New York, New York: Norton. p. 278. ISBN 9780393918472.