Only one I remember is the Sino-Vietnamese war, which to be fair was awful.

Started one and won. Against poverty.

In a more conventional sense, does it matter what ‘started’ means? And would it only count if it was today’s developed PRC?

Maybe the short conflict they had with Vietnam? Though it’s arguable whether they started it or Vietnam did. Vietnam did attack Cambodia which was a Chinese ally at the time. Imo Vietnam was justified to intervene in Cambodia because of what was happening there, but this does mean that legally China then going into Vietnam is not a clear cut case of who started it and could be construed as a retaliatory reaction. Overall the foreign policy of the PRC at that time was not great, the Sino-Soviet split led to China making some poor choices. But is nothing compared to what the US has done and all of the wars they started (and don’t forget that the Europeans were also deeply involved with helping the US in most of its wars). For being as powerful as it is, China is one of the most peaceful countries in the world.

Anticommunists would likely argue that the Chinese military incursion into Tibet in the early 1950s constituted a war, but I am unaware of any states recognising it as such. The centrist John Powers’s History as Propaganda notes that ‘though Chinese troops had entered Tibet numerous times at the behest of Tibetan governments prior to the 1950s, [some see] no contradiction in denying China a right to send in its military while arguing that Britain’s military incursion was legitimate.’

P.S. If you want to go through the candidates, you can skim here. Note, though, that not all of these conflicts would legally qualify as wars, and the PRC’s responsibility for any, like the Sino-Indian War, is quite arguable.