I figured it out. I've added a state 'waitingForToken' that is initially true.

    const [user, setUser] = useState(null);
    const [waitingForToken, setWaitingForToken] = useState(true);
    const refreshToken = useCallback(refresh, []);

In refresh(), I set the state to false.

    async function refresh() {
        try {
            const {
                data: { user, ...rest },
            } = await axios.post('refresh-token', {}, { withCredentials: true });
            setUser(user);
            setToken(rest);
        }
        finally {
            setWaitingForToken(false);
        }
    }

And export it:

    return {
        user,
        waitingForToken,
        setUser,

Then in my App:

const App = () => {
    const { waitingForToken } = AuthContainer.useContainer();
    return (waitingForToken ? <div/> :
        <Switch>
            <Route path="/login" component={Login} />
            <ProtectedRoute exact={true} path="/" component={Dashboard} />
            <ProtectedRoute path="/settings" component={Settings} />
            <ProtectedRoute component={Dashboard} />
        </Switch>                
    );

Hope this can help someone!