Get the automatic excerpt from a page created with gutenberg

You can hook the get_the_excerpt filter with parse_blocks to extract the content of your post.

add_filter( 'get_the_excerpt', 'se378694_default_excerpt', 10, 2 );

function se378694_default_excerpt( string $post_excerpt, WP_Post $post ):string {
    if ( empty( $post_excerpt ) ) {
        $blocks = parse_blocks( $post->post_content );

        // check if the first block matches the type of content you want for your excerpt
        if ( ... ) {
            $post_excerpt = render_block( $blocks[ 0 ] );
        }
    }
}

You can use render_block() if you want to get the final content of any block in your post content.

And parse_blocks() to convert the post content (string) into an array of blocks.