How to navigate to first/default route of GoRouter StatefulShellBranch

Question

I'm using a StatefulShellRoute with StatefulShellBranches as in the code below.

I would like to achieve the following: when I am inside a route in a StatefulShellBranch I want to navigate to the first/default route for that StatefulShellBranch. For example, when I have navigated to path5, from inside Widget5 I want to navigate to path4.

My use case is, I have a back button inside Widget5, and when I directly navigate to path5 (i.e. via a deep link), I want to "pop" to the first/default route within the StatefulShellBranch when the back button is pressed.

Router

router = GoRouter(
    routes: StatefulShellRoute.indexedStack(
      parentNavigatorKey: parentNavigatorKey,
      branches: [
        StatefulShellBranch(
          navigatorKey: key1,
          routes: [
            GoRoute(
              path: path1,
              pageBuilder: (context, state) {
                return Widget1();
              },
              routes: <RouteBase>[
                GoRoute(
                  path: path2,
                  pageBuilder: (context, state) {
                    return Widget2();
                  },
                ),
                GoRoute(
                  path: path3,
                  pageBuilder: (context, state) {
                    return Widget3();
                  },
                ),
              ],
            ),
          ],
        ),
        StatefulShellBranch(
          navigatorKey: key2,
          routes: [
            GoRoute(
              path: path4,
              pageBuilder: (context, state) {
                return Widget4();
              },
            ),
            GoRoute(
              path: path5,
              pageBuilder: (context, state) {
                return Widget5();
              },
            ),
          ],
        ),
      ],
    ),
    GoRoute(
      parentNavigatorKey: parentNavigatorKey,
      path: path6,
      pageBuilder: (context, state) {
        return Widget6();
      },
    ));

Widget

// Inside Widget5
class BackButton extends StatelessWidget {
  ...
  onPressed() {
    if (router.canPop()) {
      router.pop();
    } else {
      // TODO: Navigate to default route of StatefulShellBranch
      final defaultRoute = router
          .routerDelegate
          .currentConfiguration.???();
    }
  }
  ...
}