How to Access wp_usermeta Data Immediately After a New User is Created

The edit_user_created_user will work for when adding users via user-new.php:

add_action( 'edit_user_created_user', 'wpse_edit_user_created_user', 10, 2 ); //for user-new.php page new user addition
function wpse_edit_user_created_user( $user_id, $notify ) {
    $meta = get_user_meta( $user_id, 'my_field', true );
}

For the sake of completeness, I used the following code for testing the user meta data, which I grabbed from this answer.

/**
 * Declaring the form fields
 */
function show_my_fields( $user ) {
   $fetched_field = get_user_meta( $user->ID, 'my_field', true ); ?>
    <tr class="form-field">
       <th scope="row"><label for="my-field"><?php _e('Field Name') ?> </label></th>
       <td><input name="my_field" type="text" id="my-field" value="<?php echo esc_attr($fetched_field); ?>" /></td>
    </tr>
<?php
}
add_action( 'show_user_profile', 'show_my_fields' ); //show in my profile.php page
add_action( 'edit_user_profile', 'show_my_fields' ); //show in my profile.php page

//add_action( 'user_new_form_tag', 'show_my_fields' ); //to add the fields before the user-new.php form
add_action( 'user_new_form', 'show_my_fields' ); //to add the fields after the user-new.php form

/**
 * Saving my form fields
 */
function save_my_form_fields( $user_id ) {
    update_user_meta( $user_id, 'my_field', $_POST['my_field'] );
}
add_action( 'personal_options_update', 'save_my_form_fields' ); //for profile page update
add_action( 'edit_user_profile_update', 'save_my_form_fields' ); //for profile page update

add_action( 'user_register', 'save_my_form_fields' ); //for user-new.php page new user addition