Is there any way to use (default) SearchView in TextInputLayout?

I would like to use this "fancy" TextInputLayout around my SearchView (more precisely around my text which appears in the SearchView).

By default in the TextInputLayout only EditText (or descendant) works fine (for instance the options to personalize error messages, or hints, etc.)

In the .xml file:

<com.google.android.material.textfield.TextInputLayout
    android:layout_width="match_parent"
    android:layout_height="wrap_content">
    <SearchView
        android:id="@+id/searchView"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />
</com.google.android.material.textfield.TextInputLayout>

The actual output is a simple SearchView (exactly the same as without TextInputLayout), but I would like to expect a more customizable text.