Thử đi.
Hoa tiêu
Tạo điều hướng tùy chỉnh.
@Navigator.Name("custom_fragment")  
class CustomNavigator(
    private val context: Context,
    private val manager: FragmentManager,
    private val containerId: Int
) : FragmentNavigator(context, manager, containerId) {
    override fun navigate(destination: Destination, args: Bundle?, navOptions: NavOptions?) {
        val tag = destination.id.toString()
        val transaction = manager.beginTransaction()
        val currentFragment = manager.primaryNavigationFragment
        if (currentFragment != null) {
            transaction.detach(currentFragment)
        }
        var fragment = manager.findFragmentByTag(tag)
        if (fragment == null) {
            fragment = destination.createFragment(args)
            transaction.add(containerId, fragment, tag)
        } else {
            transaction.attach(fragment)
        }
        transaction.setPrimaryNavigationFragment(fragment)
        transaction.setReorderingAllowed(true)
        transaction.commit()
        dispatchOnNavigatorNavigated(destination.id, BACK_STACK_DESTINATION_ADDED)
    }
}
NavHostFragment
Tạo NavHostFragment tùy chỉnh.
class CustomNavHostFragment: NavHostFragment() {
    override fun onCreateNavController(navController: NavController) {
        super.onCreateNavController(navController)
        navController.navigatorProvider += PersistentNavigator(context!!, childFragmentManager, id)
    }
}
navigation.xml
Sử dụng thẻ tùy chỉnh thay vì thẻ phân đoạn. 
<navigation xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto" android:id="@+id/navigation"
    app:startDestination="@id/navigation_first">
    <custom_fragment
        android:id="@+id/navigation_first"
        android:name="com.example.sample.FirstFragment"
        android:label="FirstFragment" />
    <custom_fragment
        android:id="@+id/navigation_second"
        android:name="com.example.sample.SecondFragment"
        android:label="SecondFragment" />
</navigation>
bố cục hoạt động
Sử dụng CustomNavHostFragment thay vì NavHostFragment.
<androidx.constraintlayout.widget.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    android:id="@+id/container"
    android:layout_width="match_parent"
    android:layout_height="match_parent">
    <fragment
        android:id="@+id/nav_host_fragment"
        android:name="com.example.sample.CustomNavHostFragment"
        android:layout_width="0dp"
        android:layout_height="0dp"
        app:layout_constraintBottom_toTopOf="@+id/bottom_navigation"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toTopOf="parent"
        app:navGraph="@navigation/navigation" />
    <com.google.android.material.bottomnavigation.BottomNavigationView
        android:id="@+id/bottom_navigation"
        android:layout_width="0dp"
        android:layout_height="wrap_content"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintStart_toStartOf="parent"
        app:menu="@menu/navigation" />
</androidx.constraintlayout.widget.ConstraintLayout>
Cập nhật
Tôi đã tạo dự án mẫu. liên kết
Tôi không tạo NavHostFragment tùy chỉnh. Tôi sử dụng navController.navigatorProvider += navigator.