For a bottom-up argument, consider mostly text based media like twitter or whatsapp. If you're involved in similar tech, I think it's quite easy to roughly estimate both the development and infrastructure requirements for something like this. It isn't too different from an email service or another text-centric media. Also (like email) it lends well to a distributed architecture, so may not even need a centralized infrastructure.
Hosting and serving video is costlier. Again, distributed architecture can make this irrelevant, or a much smaller. Even assuming a Facebook clone though, hard costs like video streaming are a small fraction of facebook revenue.
Re: distributed architecture. Remember that this is what the internet/web is fundamentally designed to do. It's not radical, and there are working examples out there that will work at massive scale. The www itself is such an example, but there are also more explicit examples that work more like Facebook does.
For a comparative argument, consider FB or Twitter when they were much (revenue-wise) smaller. Consider minor social networks (like HN). These might have 1/100th of FB or Twitter's usage, but generally operate on orders of magnitude less revenue user-for-user.
Basically, there are enough demonstrative examples to convince me that it is possible, even trivial.
I think there may be a lot more aspects to it that need attention than one anticipates at first.