Hi there!
You would need to create a template override for that email and just move some of the do_actions
in the template around.
If you open the email under WooCommerce > Settings > Emails > New Order you will see an option right at the bottom to copy the template to your theme and the location if will be copied to – https://docs.woocommerce.com/document/template-structure/#section-1

Link to image: https://d.pr/i/5qJw8x
When you edit the template then, you can move the do_action( 'woocommerce_email_customer_details', $order, $sent_to_admin, $plain_text, $email );
to the top like this and it will show the customer details first;
/*
* @hooked WC_Emails::customer_details() Shows customer details
* @hooked WC_Emails::email_address() Shows email address
*/
do_action( 'woocommerce_email_customer_details', $order, $sent_to_admin, $plain_text, $email );
/*
* @hooked WC_Emails::order_details() Shows the order details table.
* @hooked WC_Structured_Data::generate_order_data() Generates structured data.
* @hooked WC_Structured_Data::output_structured_data() Outputs structured data.
* @since 2.5.0
*/
do_action( 'woocommerce_email_order_details', $order, $sent_to_admin, $plain_text, $email );
/*
* @hooked WC_Emails::order_meta() Shows order meta data.
*/
do_action( 'woocommerce_email_order_meta', $order, $sent_to_admin, $plain_text, $email );
The order notes are part of do_action( 'woocommerce_email_order_details', $order, $sent_to_admin, $plain_text, $email );
and you would need to reach out to a developer if you would like to show that somewhere else.