TextInputLayout and AutoCompleteTextView

A little late, but yes, you'll have to roll your own implementation. The good news is that this is fairly straightforward. Here's how TextInputEditText was implemented:

https://android.googlesource.com/platform/frameworks/support.git/+/master/design/src/android/support/design/widget/TextInputEditText.java

Accordingly, here's what TextInputAutoCompleteTextView might look like.

public class TextInputAutoCompleteTextView extends AppCompatAutoCompleteTextView {

    public TextInputAutoCompleteTextView(Context context) {
        super(context);
    }

    public TextInputAutoCompleteTextView(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    public TextInputAutoCompleteTextView(Context context, AttributeSet attrs, int defStyleAttr) {
        super(context, attrs, defStyleAttr);
    }

    @Override
    public InputConnection onCreateInputConnection(EditorInfo outAttrs) {
        final InputConnection ic = super.onCreateInputConnection(outAttrs);
        if (ic != null && outAttrs.hintText == null) {
            // If we don't have a hint and our parent is a TextInputLayout, use it's hint for the
            // EditorInfo. This allows us to display a hint in 'extract mode'.
            final ViewParent parent = getParent();
            if (parent instanceof TextInputLayout) {
                outAttrs.hintText = ((TextInputLayout) parent).getHint();
            }
        }
        return ic;
    }
}

Now, with AndroidX you don't need customise something.
Need just add material component style (was added in 1.1.0-alpha06, see release notes).

<com.google.android.material.textfield.TextInputLayout
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:hint="Example TextInputLayout">

    <androidx.appcompat.widget.AppCompatAutoCompleteTextView
    style="@style/Widget.MaterialComponents.AutoCompleteTextView.FilledBox"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"/>

</com.google.android.material.textfield.TextInputLayout>