You’re thinking of it in terms of a so-called “market socialist” economy, which shouldn’t be confused with socialism, such as the socialist market economies like in China which are socialist. Either way, depending on the stage in socialist construction, either you can still open a company providing it’s in a sector deemed acceptable by the socialist system to expand market-wise, or the state itself can create new industries and firms.

If all your daily needs are met without you having to worry about it, people will have the freedom to just group and start projects, business, productions of whatever they would like or need. Instead of only founder’s owning the company, all workers own it and have democratic power to steer it.

Workers owning the means of production is not an overly prescriptive idea. It means the bourgeois have been deposed or substantially oppressed such that workers actually dictate production. This is only really possible for a society after a revolution, as the bourgeois ruling class will not allow themselves to be deposed or substantially oppressed otherwise.

This is one of the more flexible and interesting ways in which socialists can experiment. Experiments have ranged pretty widely. Some subgroups tried forms of primitivist agricultural communalism, though this can only exist for any significant duration under the protection of an industrialized state. In the context of industrialized production it can look like co-ops or state-run enterprises or various forms of oppressed bourgeois or all of the above simultaneously at different levels of productive forces (start more bourgeois and get stripped of it as production becomes so developed it can be more easily run via planning). Chile wanted to experiment with cybernetics developed with Stafford Beer before being murdered by US-backed fascists, the left leadership murdered in the tens of thousands following this. Can’t stress enough the importance of that revolution part - Allende rose via liberal democratic means and capitalists asserted the true basis of their rule, which is violence and coercion.

So to answer your question, it would probably look petty bourgeois at first (individuals incorporating a business) under most near term circumstances, and does in countries run by socialists, but what to do as the enterprise grows varies. And sometimes a state may coordinate production even early on. For example important technologies may be developed by university researchers and to enter production they are state-funded and forced to collaborate with other researchers, with a petty bourgeois payoff (salary, ownership that dwindles until it enters a certain tier, etc). The latter also happens under capitalism but the profits are entirely privatized, capital feeds off the state funding, whereas the point of this industrial policy in socialist states is to either build missing productive capacity, to socialize much of the gains, and eventually turn over to co-ops and state-run enterprise, etc.

You would gather a worker community of like minded people who agree a new company is needed. Pool your resources, and coordinate building the company.