First Paragraph as an Excerpt

add_filter( 'wp_trim_excerpt', 'my_custom_excerpt', 10, 2 );
 
function my_custom_excerpt($text, $raw_excerpt) {
    if( ! $raw_excerpt ) {
        $content = apply_filters( 'the_content', get_the_content() );
        $text = substr( $content, 0, strpos( $content, '</p>' ) + 4 );
    }
    return $text;
}

Source