Any regime that is in name Marxist/ Communist.
Well then, the answer is as OTL: as soon as some pseudo-military dictatorship that's already isolated and has pissed off the nobility decides that it can earn itself international recognition, legitimacy and aid (at least from foreign Marxists) it otherwise wouldn't get by proclaiming itself to be such.
I don't see a regime deciding to declare itself specifically Marxist until maybe the Second International in 1889, which established Marxism as the dominant face of socialist thought and as enjoying enough popularity to give such a regime what they wanted.
The Brazilian Empire fell to a Positivist military coup that same year and would probably be the earliest chance to make this happen; a more left-wing Positivist regime would probably operate quite similarly to Marxism-Leninism and could probably justify calling itself Marxist if it had a reason to.