English language is not shown at first shot...

The problem is that the module assumes that the original page is in English, and won't initially offer to translate in the current language.
Once you select another language, the page is no more in English, so it will appear in the selector.

I fixed it by hard-coding my site language in google_translator.module (French in my case):

164   unset($active_langages[0]);
165   if (!empty($active_langages)) {
166     $display_mode = variable_get('google_translator_active_languages_display_mode', '');
167     $display_mode = !empty($display_mode) ? 'layout: google.translate.TranslateElement.InlineLayout.' . $display_mode : '';
168     $default = "<span id='google_translator_element' class='google_translator'>{$close}</span><script>function googleTranslateElementInit() {
169   new google.translate.TranslateElement({
170     pageLanguage: 'fr',                                // <-- set site language here
171     includedLanguages: '" . implode(',', array_keys($active_langages)) . "'," . $display_mode . " }, 'google_translator_element');}</script>
172     <script src='//translate.google.com/translate_a/element.js?cb=googleTranslateElementInit'></script>";
173   }
174   return $default;
175 }

Ideally this should be a module configuration parameter

I have developed a patch.

Drupal::languageManager()->getCurrentLanguage()->getId() gets the current language code of the website. This can be passed to drupalSettings.googleTranslatorElement and used as pageLanguage for the new TranslateElement.

It would also be possible to leave pageLanguage undefined. Then google tranlsate will automatically set the source language.

Based on the patch from #7 I developed a patch which uses dependency injection instead of the static Drupal::languageManager() call. Since Tenguiz has found the actual solution to the problem please give credit to him (also?).

Provided Patch #9 resolving the issue as google translator list eng. not shown at first shot, now after the patch in the dropdown selector show English option at first when Spanish language enabled firstly.
RTBC+1

Can someone please review this and set the issue to "Reviewed & tested by the community"?

This is really great work, I appreciate it, y'all. Thanks!

Automatically closed - issue fixed for 2 weeks with no activity.