Imagine an ark ship carrying the entire remaining human population, about a quarter million. Everything they need to start a colony is aboard the ark. They arrive at a new planet, completely disconnected from any previous economy. The people receive shelter and food supplies from the ark, subsistence/survival is their initial motivation. At some point, industries are established and valuable resources are being collected. A colonial representative government receives and redistributes the resources; raw resources go to processors, then on to manufacturers, for instance. At what point and how did the economic system shift to ownership and capitalism without physical conflict? Or is conflict inevitable?
You have asked an interesting (and open-ended) question to begin with. An issue with answering questions regarding capital and Socialism is that they get lost in the political thicket, although given the nature of the question, politics is inevitable at some point. No matter how much I appreciate the 'ark ship' narrative, I would like to answer without delving into it. [Opinion alert: The following piece will be subjective.]
It is important to have a basic understanding of the context. For a reader not familiar with the 'chronology' of Capitalism and Socialism, I would strongly recommend the following tutorial for a basic but effective crash course about the subject before we proceed. The video has a classic American style of storytelling [https://www.youtube.com/watch?v=B3u4EFTwprM].
Capitalism predates Socialism. During my undergraduate days, my easily impressionable learned that the history of Capitalism began with the French Revolution (1789) and Robespierre, although this was not entirely true. Capitalism and its supporters argued that if humans are left to their own without any other external intervention, their agreement on resource sharing, institutions, and operations will be very similar to what Capitalism proposes. It is the central idea behind economics' widely used 'market.' Capitalists believe it is rational agents' human nature to participate in markets.
Industrial Capitalism in Britain in the late eighteenth century and later in Western Europe and the United States is associated with the discovery and large-scale usage of the steam engine. Profit, productivity, cost efficiency, and scale became intertwined with human lives. But it soon posed other challenges for society to grapple with: fairness in profit sharing, fight over resources, inhuman working hours, and child labor.
Socialism as an intellectual construct began in the nineteenth century mainly as a critique and response to Capitalism. Socialists were opposed to the idea of humans as profit-maximizing economic agents. Early Socialism imagined people thrive in social cohesion, driven by ideas beyond personal gains, and do not always act as 'rational agents' in its economic sense. Socialist thinkers thought Capitalism reduced the basic 'identity of a man' to a cog in an industrial-sized wheel. The early socialists did not imagine an industrious progeny like Stalin. Here I would like a small digression to put things in historical context: During the 1950s, when the world was divided into Capitalist vs. Socialist camps, the first and a Socialist Prime Minister of independent India said that 'profit is a dirty word.'
Finally, to answer your question, can Capitalism and Socialism exist separately? The answer is yes. One can look at the USA and the USSR during the cold war. But can they exist together without conflict? By construction, the answer is an obvious no. Imagine a socialist Texas and a capitalist Florida! During the latter half of the twentieth century, we have seen several Latin American, African, and Asian countries oscillating between the two systems with every regime change. It hardly requires an economist to evaluate those changes that altered people's lives.