cannot declare objects inside an object of a Class in javascript

You can define instance fields with that syntax (outside of the constructor), but not mutate them. Don't confuse the = syntax with the usual assignment syntax, as it really has different rules. For instance you can also use this syntax:

class A {
    ["obj"] = {};
}

If you want to mutate fields/properties, you'll have to do this inside the constructor or other method. On the other hand, nothing stops you to initialise the field with a more elaborate object literal.

NB: to create an instance you should use the new keyword.

So either do:

class A {
    obj = { x: 0 };
}

let a = new A();
console.log(a.obj.x);

Or do:

class A {
    obj = {};
    constructor() {
        this.obj.x = 0;
    }
}

let a = new A();
console.log(a.obj.x);