How old is the idea that humans have 360 joints?

The idea that humans have 360 joints appears to derive from ancient Chinese cosmology. Notice what Dong Zongshu says more fully when he makes this statement;

Man has 360 joints which match the number of heaven. ... He has ears and eyes above, with their keen sense of hearing and seeing, which resemble the sun and the moon. His body has its orifices, which resemble rivers and valleys. His heart has feelings of sorrow, joy, pleasure, and anger, which are analogous to the spiritual feelings [of Heaven]. As we look at man's body, how much superior it is to that of other creatures and how similar to Heaven!... Man is distinct from other creatures and forms a trinity with Heaven and Earth ... The agreement of Heaven and Earth and the correspondence between yin and yang are ever found complete in the human body. The body is like Heaven. Its numerical categories and those of Heaven are mutually interlocked ... Internally the body has five viscera, which correspond to the five agents. Externally there are four limbs, whichc orrespond to the four seasons. The alternating of opening and closing the eyes corresponds to day and night ... [and] the alternating of sorrow and joy corresponds to yin and yang.... In what may be numbered, there is correspondence in number. IN what may not be numbered, there is correspondence in kind. (Quoted in Richard Smith, Fortune-tellers and Philosophers Divination In Traditional Chinese Society, Taylor & Francis 2021.)

As many scholars of the subject have pointed out, Dong Zongshu considers the human body as a microcosm of the universe. Dong Zongshu came to the belief that humans have 360 joints on the basis that the 360 days of the Earth (in his traditional calendar) have some sort of correspondence to the human body, and this is how he identified it. If we go through some other ancient Chinese texts, we find similar statements to this effect. For example, in a text from the 1st century BC known as the Lingshu Jing (or the Divine Pivot), it’s said that “[i]n the year there are 365 days; human beings have 365 joints” (Bary & Blom, Sources in Chinese Tradition, Vol. 1, 1999, 2nd ed., pg. 276). So, this author identified the year as having 365 days, and so correspondingly stated that humans have 365 joints. The parallelism and basis for the origins of this number is clear and is based very much on the Chinese cosmology of this period of the human body as a microcosm of the universe writ large. Yet another source exists on the subject. The following is from the Huainanzi which was written in the 2nd century BC, and purports to quote the ancient Chinese philosopher Laozi (who lived in the 6th century BC);

Laozi said: Man is born in the change of Heaven and Earth, ... his head is round modeled on heaven, his feet are square just like earth. Nature has four seasons, five elements, nine stars, and three hundred and sixty days, man has four limbs, five zang organs, nine apertures, and three hundred and sixty parts. Nature has winds and rains, and is affected by cold and heat; man has likes and dislikes, and is affected by joy and anger. The gallbladder is the cloud, and the lung the air, the spleen the wind, the kidney the rain, and the liver the thunder. Man is similar to Heaven and Earth in kind, and the heart is his master. His ears and eyes are the sun and moon, and his blood and qi are rain and wind. (Ning Yu, The Chinese HEART in a Cognitive Perspective Culture, Body, and Language, De Gruyter 2009, pg. 42)

Although it purports to quote Laozi, there is evidence that the Chinese cosmology of the human body as a microcosm of the universe goes back to the Han dynasty and so this is roughly the period that this idea may have emerged in (and makes sense given the date of these texts). It's possible the idea is earlier but I'm not aware of any indications that it is.