Sure thing:
type GenericObject = { [key: string]: any };
let myVariable1: GenericObject = 1; // Type 'number' is not assignable to type '{ [key: string]: any; }'
let myVariable2: GenericObject="abc"; // Type 'string' is not assignable to type '{ [key: string]: any; }'
let myVariable3: GenericObject = {} // OK
let myVariable4: GenericObject = {name: 'qwerty'} //OK
(code in playground)