How to change the background colour for MaterialCardView using the style.xml file?

Create your custom style for MaterialCardView that extends Widget.MaterialComponents.CardView:

<style name="YourCardView" parent="Widget.MaterialComponents.CardView">
    <item name="cardBackgroundColor">@color/your_color</item>
</style>

Then you can set this style manually to your single MaterialCardView in xml layout:

<com.google.android.material.card.MaterialCardView
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    style="@style/YourCardView">
        <!-- card content -->
</com.google.android.material.card.MaterialCardView>

Or you can set the style for all MaterialCardViews within your custom theme (that extends a theme from MaterialComponents):

<style name="YourTheme" parent="Theme.MaterialComponents.Light.NoActionBar">
    <item name="materialCardViewStyle">@style/YourCardView</item>
</style>

Widget.MaterialComponents.CardView can be styled just alike any other component:

<style name="CustomCardView" parent="Widget.MaterialComponents.CardView">
    <item name="cardBackgroundColor">?attr/colorSurface</item>
</style>

Changing colorSurface, which defaults to #FFFFFF, might be rather effective for a dark theme.

see the documentation, which also explains how to apply it to all instances.