Having been down this path several times (small company to acquisition to growth), if you actually sit down during the startup phase and list all of the features/processes that would make your product fully mature, you're looking at a massive project with a lot of people involved. By 'fully mature' I mean it meets the needs of the average customer in your target market.
The sweet spot for a startup is if you can look at that big mess of features and find something actually do-able by a small team that can still meet the needs of some portion of your target market.
When you've achieved that, you can then start filling in the rest of the features that will fill the needs of the rest of your market. This is where the headcount can grow significantly, because even small line items in the feature set could involve a big project, yet still be justified because you have enough potential or actual revenue to justify the team growth. Once you're in this phase, the communication overhead of adding people and teams also forces the creation of meta-teams to support the rest of the teams...and there you have it, you now have a lot of people.
> it meets the needs of the average customer in your target market
In most markets, the average customer is a minority of customers. There is a lot of variety in each niche's demand. Maturity is having market coverage of those niches. Whether that coverage needs to be done by a single company is another question.
Obviously. But even in a company with just 13 people building filters, the employees need to get paid, get health insurance, desks, chairs and computers. Engineers need servers, databases, monitoring, pagers. That's the part that they outsourced then, and now FB manages for them.
For example, when Instagram was purchased by Facebook they only had 13 employees and now they have something like 500.