Short answer is No and Yes.
It depends on what do you mean? Do you mean the Facebook/Instagram application? Then yes. There are a gazillion tutorials on the internet which will teach you how to develop a facebook / instagram or twitter clone. And you can pretty much create a 1:1 feature app in less than a month. The problem isn't that one developer can create these or not, the problem is a single developer can't market his app so the whole world starts using it. Basically you'll write the program, and nobody will use it.
You need marketing people to convince the world that they need your product or service.. That's why marketing is every bit as important as development is at companies like Instagram etc. One might even say it's more important. Any half decent programmer can write Twitter, it's completely trivial compared writing something like PhotoShop or Final Cut Pro.
As a tech entrpreneur, you'd should as good at marketing as you are at programming.
Facebook, Instagram or Twitter are not just code. It's simple to build an app yourself if you have the skills, it's much harder to build a company around it that is successful.
Don't fall into the trap of believing you can make a successful app that will make a lot of money - companies make money, not apps. And it takes a shit-ton of more to make a successful company than a good idea and good code.
Facebook didn't buy Instagram for $1 billion because it was good code, they bought it because it was a successful company.
Conclusion: coding up an app that is superficially similar to Instagram is probably simple, but to create a well-rounded app that actually works for so many users and can stay ahead of the competition is much, much more difficult, and I would say impossible for a single person. This effect is true even when discounting the added value from marketing and UX teams, and even when discounting for the problems that only start showing at a very large scale.
So, again, you can make the app, but so can a million other developers (and probably better than you), but if you think you can make the company by yourself? That is unrealistic.
Until next time...