Your loop rewrite is good so far, yet you can make it better:
<?php
$at_social_html="<ul class="at__social">";
/* array elements: social-media-name/meta-key => ['href-before-string', 'href-after-string', 'fa-class'] */
$author_sociables = array(
'facebook' => ['', '', 'fa-fb'],
'twitter' => ['', '', 'fa-twitter'],
'instagram' => ['', '', 'fa-instagram'],
'google' => ['//plus.google.com/', '', 'fa-google-plus'],
'pinterest' => ['//pinterest.com/', '', 'fa-pinterest'],
'tumblr' => ['//', '.tumblr.com/', 'fa-tumblr']
);
/* Loop */
foreach($author_sociables as $key=>$value){
$at_author_meta_value = get_the_author_meta( $key );
if ( $at_author_meta_value ) :
$at_social_html .= '<li><a target="_blank" class="author__social" href="'. $value[0] . esc_url( $at_author_meta_value ) . $value[1]'"><i class="fa '. $value[2] .'"></i></a></li>';
endif;
}
$at_social_html .= '</ul>';
echo $at_social_html;