Of course it's damn possible to build that with $2 billion. Will it be robust as google's infrastructure? No. Will it have (unlimited) scale as Google has? No.

Of course it's damn possible to build that with $2 billion. Will it be robust as google's infrastructure? No. Will it have (unlimited) scale as Google has? No. Will it have network connectivity and geographical distribution as Google has? No. So, if you set scope on expectations and dedicate time and resources, it's definitely possible. Reasonable? Probably not.