Is it possible to build a blockchain explorer to put on aws?
There are open-source projects available that make building your own query service possible. A good example would be Libbitcoin, see their github and official website.

You need to install libbitcoin server - this is a full bitcoin node with a database, and libbitcoin explorer - a set of tools among which you will find one for querying the server about addresses (balances and whatnot).

Be aware that the server will download the whole blockchain. It is not possible to have your own query server without having the blockchain on hand.