Prototype to land as part of AMP Optimizer. See https://github.com/ampproject/amp-toolbox-php/issues/176

amp-elevate-resource-hints.php

<?php
/**
 * AMP Elevate Resource Hints plugin bootstrap.
 *
 * @package   Google\AmpElevateResourceHints
 * @author    Weston Ruter, Google
 * @license   GPL-2.0-or-later
 * @copyright 2021 Google Inc.
 *
 * @wordpress-plugin
 * Plugin Name: AMP Elevate Resource Hints
 * Plugin URI: https://gist.github.com/westonruter/8a171f6c561fd69ac33a032983dafaf3
 * Description: Prototype transformer which elevates <code>link</code> elements to <code>Link</code> response headers. This functionality will be incorporated into the Optimizer via <a href="https://github.com/ampproject/amp-toolbox-php/issues/176">amp-toolbox-php#176</a>.
 * Version: 0.1.1
 * Author: Weston Ruter, Google
 * Author URI: https://weston.ruter.net/
 * License: GNU General Public License v2 (or later)
 * License URI: http://www.gnu.org/licenses/gpl-2.0.html
 * Gist Plugin URI: https://gist.github.com/westonruter/8a171f6c561fd69ac33a032983dafaf3
 */

namespace Google\AmpElevateResourceHints;

use AmpProject\Optimizer;

/**
 * Filter configuration array to register the transformer.
 *
 * @param array $configuration Associative array of configuration data.
 * @return array Configuration.
 */
function filter_amp_optimizer_config( array $configuration ) {
	require_once __DIR__ . '/ElevateResourceHints.php';
	$configuration[ Optimizer\Configuration::KEY_TRANSFORMERS ][] = ElevateResourceHints::class;
	return $configuration;
}

if ( empty( $_GET['amp_disable_elevate_resource_hints'] ) ) { // phpcs:ignore WordPress.Security.NonceVerification.Recommended
	add_filter( 'amp_optimizer_config', __NAMESPACE__ . '\filter_amp_optimizer_config', PHP_INT_MAX );
}

ElevateResourceHints.php

<?php
/**
 * Elevate resource hints from link elements to headers.
 *
 * @link https://github.com/ampproject/amp-toolbox-php/issues/176
 * @package Google\AmpElevateResourceHints
 */

namespace Google\AmpElevateResourceHints;

use AmpProject\Dom\Document;
use AmpProject\Optimizer\ErrorCollection;
use AmpProject\Optimizer\Transformer;
use AmpProject\Attribute;
use AmpProject\Dom\Element;
use DOMAttr;

/**
 * This is a hack to send headers as part of a transformer! This is only needed because the transformer doesn't currently
 * take a collection for mutating the HTTP headers. See <https://github.com/ampproject/amp-toolbox-php/issues/176#issuecomment-812142640>.
 */
final class ElevateResourceHints implements Transformer {

	/**
	 * Attributes from link elements (other than href) to surface to Link header.
	 *
	 * @var string[]
	 */
	const ELEVATED_LINK_ATTRIBUTES = [
		Attribute::AS_,
		Attribute::CROSSORIGIN,
		Attribute::IMAGESIZES,
		Attribute::IMAGESRCSET,
		Attribute::REFERRERPOLICY,
		Attribute::REL,
		'integrity',
		'prefetch',
	];

	/**
	 * Link relations that should get elevated to Link headers.
	 *
	 * @var string[]
	 */
	const ELEVATED_LINK_RELATIONS = [
		Attribute::REL_DNS_PREFETCH,
		Attribute::REL_PRECONNECT,
		Attribute::REL_PRELOAD,
		Attribute::REL_MODULEPRELOAD,
	];

	/**
	 * Apply transformations to the provided DOM document.
	 *
	 * @param Document        $document DOM document to apply the transformations to.
	 * @param ErrorCollection $errors   Collection of errors that are collected during transformation.
	 */
	public function transform( Document $document, ErrorCollection $errors ) {

		$links = $document->xpath->query( './link[ @rel and @href ]', $document->head );
		foreach ( $links as $link ) {
			/** @var Element $link */
			$relations = preg_split( '/\s+/', trim( $link->getAttribute( Attribute::REL ) ) );
			if ( 0 === count( array_intersect( $relations, self::ELEVATED_LINK_RELATIONS ) ) ) {
				continue;
			}

			$header = sprintf( 'Link: <%s>', esc_url_raw( $link->getAttribute( Attribute::HREF ) ) );
			foreach ( $link->attributes as $attribute ) {
				/** @var DOMAttr $attribute */
				if ( in_array( $attribute->nodeName, self::ELEVATED_LINK_ATTRIBUTES, true ) ) {
					$header .= sprintf( '; %s="%s"', $attribute->nodeName, addcslashes( $attribute->nodeValue, '"\\' ) );
				}
			}

			header( $header, false );
			$link->parentNode->removeChild( $link );
		}
	}
}

Installation instructions: https://gist.github.com/westonruter/6110fbc4bef0c4b8c021a112012f7e9c