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.