One of the sources of the alternation between stop and nasal codas—the ‘陽入對轉’ of traditional Chinese phonology—is assimilation of a final stop to the nasal initial of the following word. An example is the expression zhēng yuè 正月 ‘first month of the lunar year’. The earliest secure occurrence of 正月 I am aware of, referring to the first month, is in the Luan Shu Fou 䜌書缶, a Zhou bronze inscription:「正月季春元日」’on the first day of the first month’. Palaeographers would probably know earlier ones. The character 正 normally writes *teŋ-s > tsyeng > zhèng ‘correct (adj., v.)’. How did it become used to express the meaning ‘first’ ?
There is in Western Sino-Tibetan (a.k.a. ‘Tibeto-Burman’) a root for ‘one’ which the STEDT website reconstructs as
#2726 PTB *tyak ⪤ *g-t(y)ik ONE (provisional).
The corresponding Chinese root reconstructs as *tek ‘single, only, only one’. It includes these words:
隻 *tek > tsyek > zhī ‘single’ 1260c, 適 *s-tek > syek > shì ‘only’ 0877s, 啻 *s-tek-s > syeH > shì ‘only’ 0877k.
Root *tek and the root in 正 *teŋ-s differ only in the nasality of the coda. This suggests 正 writes 隻 *tek ‘1’ in a context where its ending had become nasalized. The onset of the following word: 月 *[ŋ]ʷat is likely where nasality comes from. 正月 was an appropriate way of putting *teŋ-ŋʷat < *tek-ŋʷat into readable form.
Liu Shiru. 1965. Weijin Nanbei chao liangci yanjiu (Studies on Classifiers in Wei-Jin and Nan-Bei dynasties). Beijing: Zhonghua.