All of this is more or less true, but they come with caveats:
-You're correct in that capitalist countries would have a head start, but even when countries have been rebuilt from ground zero, capitalist countries tend to have come up on top. We can compare West and East Germany (feel free to extend this to all of Europe post-WWII if you want), North and South Korea, Hong Kong vs. Mainland China (similar with Taiwan vs. China), and recently, I've seen the Cuba vs. Singapore analogy. In every one of those examples, the capitalist country has ended up doing better than the socialist country, even with similar starting points. Even with China, the greatest poverty reduction in human history (by raw number) occurred when China opened up its economy for foreign investment. And to use another example listed, communist North Vietnam did conquer capitalist South Vietnam, but Vietnam's poverty began to fall when, again, its economy became more liberal.
-You're also correct in that socialism is, in part, a reaction to capitalism. And to clarify, mixed economies tend to do the best (again, China reduced poverty when opening up its economy, it didn't go full neoliberal to do it). And yes, you're correct that various nations had a bitter taste towards capitalism after gaining independence (Africa is a key example). Again, though, if we're pitting the systems against each other, capitalism seems to have done better (see the examples above). Or, more specifically, mixed economies seem to do the best.
-If we define "post-empire" as the end of WWII, I'm not sure if capitalism can said to have had dominance per se. The capitalist and communist blocs were just as unwilling to trade with each other, and just as willing to fight proxy wars to prop up their respective ideologies. And if we're talking about Cuba, I mean, sure, okay, but no country is obliged to trade with another. And even then, isolation can be self-inflicted - Eritrea's under no obligation to join AFTA for instance, even though it's probably going to harm it.
So, yes, even if socialist countries started at a disadvantage, over the course of the 20th century, one did better than the other, the result being that there's only a handful of countries that could call themselves socialist left, whereas most other countries are capitalist, or, more accurately, mixed market. If we look up the Human Development Index for instance, most, if not all of the highest ranking countries can be defined as capitalist, albeit with strong social security nets. Part of why I'd argue "capitalism vs. socialism" is a false dichotomy, because on one hand, if your definition of "evil socialism" is simply stuff like medicare for all, free education, and various other social programs, all I can say is "GTFO." On the other, clearly it's possible for the government to have too much control over the economy, because there's plenty of examples in both the 20th and 21st centuries for that.
