How do I look up a cognito user by their sub/UUID?

As of today this is not possible with Cognito User Pools.

Users can only be looked up using their username or aliases. ListUsers API also allows users to be searched by providing search filters on some standard attributes but sub is not one of them.

Now it works. http://docs.aws.amazon.com/cognito-user-identity-pools/latest/APIReference/API_ListUsers.html

"sub" in list of supported attributes. Example for JavaScript:

var cog = new AWS.CognitoIdentityServiceProvider();

var filter = "sub = \"" + userSub + "\"";
var req = {
    "Filter": filter,
    "UserPoolId": "your pool id" // looks like us-east-9_KDFn1cvys
};

cog.listUsers(req, function(err, data) {
    if (err) {
        console.log(err);
    }
    else {
        if (data.Users.length === 1){ //as far as we search by sub, should be only one user.
            var user = data.Users[0];
            var attributes = data.Users[0].Attributes;
        } else {
            console.log("Something wrong.");
        }
    }
});