How do I display a PDF thumbnail as a link to the PDF without uploading the image

The PDF images created by wordpress are stored within the PDF attachment object metadata.

[
    {
        "id": 121,
        "media_type": "file",
        "mime_type": "application/pdf",
        ...
        "media_details": {
            "sizes": {
                "full": {
                    ...
                    "source_url": "<domain>/wp-content/uploads/document-name-pdf.jpg"
                }
    }
]

Extracting the image from the PDF

Adding an image block or adding a featured image to a post requires an attachment ID and not simply a url probably

An attachment ID can be created by “side loadeding” the url into the media library to create an attachement using the media_sideload_image function which can return the newly created attachment ID

• WordPress media_sideload_image function

Example

$pdf_image_url = $PDF_object -> media_details -> sizes -> full -> source_url;
$attachment_id   = media_sideload_image( 
    $pdf_image_url,
    $post_id, // the post to attach the image 
    'My image title',
    $return_type="id" 
);
$image = set_post_thumbnail( $post_id, $attachment_id );

Set Post Thumbnail

The function set_post_thumbnail( $post_id, $attachment_id ) can be used to assign an image to a post as the featured image