functions.php

function eg_do_not_activate_subscription_on_processing(){
    remove_action( 'woocommerce_order_status_processing', 'WC_Subscriptions_Manager::activate_subscriptions_for_order' );
    remove_action( 'woocommerce_order_status_processing', 'WC_Subscriptions_Order::maybe_record_order_payment' );
}
add_action( 'woocommerce_order_status_processing', 'eg_do_not_activate_subscription_on_processing', 0 ); // run on priority 0 to trigger before Subscriptions