The small firm is the original basic unit of analysis of business in economics. It is one who is more or less a price taker, trying to somewhat differentiate themselves but having a pretty short cost curve and goes up somewhat quickly. These firms are supposed to proliferate in the market, not grow. In fact, typically in economics, there isn’t really a real motivation for growth in firms other than technical or management progress that changes the cost curve such that the minimum efficient scale changes.
Now on to the real world; there are plenty of small firms, differentiated and there are interesting markets that support them. There are those places culturally oriented towards “local, independent, small” type of firms. And therefore these firms proliferate. It is not because of market competition that they spread but rather the diversity of preferences.
Where preferences somewhat tend towards a kind of homogeneity, small firms tend not to have an edge; it is scaling difficulties that keep firms small. Likewise, it is scaling difficulties that lead to proliferation of firms. The new entrant can typically be a small firm and it needs to determine what is the minimum efficient scale and rapidly work on the areas that can shift its minimum efficient scale more and more towards higher quantities of goods and services.