Auto Complete WooCommerce orders when the order contains a specific product ID.

woocommerce-order-complete-by-product-id.php

/**
 * Auto Complete WooCommerce orders when the order contains a specific product ID.
 */
add_action( 'woocommerce_thankyou', 'custom_woocommerce_auto_complete_order' );

function custom_woocommerce_auto_complete_order( $order_id ) { 

  if ( ! $order_id ) {
    return;
  }

  // add your product ID's to this array
  $product_ids = array( 3, 1 );
  
  // setup product array for intersect
  $product_array = array();

  $order = wc_get_order( $order_id );

  $order_items = $order->get_items();

  // store product id's to array
  foreach ( $order_items as $item => $value) {
    $product_array[] = $value[ 'product_id' ];
  }

  if ( array_intersect( $product_array, $product_ids ) ) {
    $order->update_status( 'completed' );
  }
}