Solved this using AJAX. Here is my updated code:
<?php
add_action('wp_ajax_quote_email_pdf', 'quote_email_pdf');
function quote_email_pdf()
{
wp_mail( $to, $subject, $message, $headers, $attachments );
die();
}
?>
<button class="button" id="downloadQuote">Send email</button>
<script>
jQuery(document).ready(function($){
const fullName = $('#quoteFullName').text();
const emailAddress = $('#quoteEmail a').text();
$('#downloadQuote').click(function(e){
e.preventDefault();
$.ajax({
url: sf_admin_ajax.sf_admin_ajax_url,
type: 'POST',
data: {
action: 'quote_email_pdf',
emailAddress: emailAddress,
fullName: fullName
},
beforeSend: function() {
$('.preloader-window').addClass('active')
},
success: function(data, textStatus, XMLHttpRequest) {
$('.preloader-window').removeClass('active')
console.log(data);
},
error: function ( MLHttpRequest, textStatus, errorThrown ) {
$('.preloader-window').removeClass('active')
console.log(errorThrown);
}
})
})
});
</script>