learn the process of recover or restore back your deleted email from gmail . your deleted email moves to trash folder once it get deleted from inbox , where it stays for a period of 30 days , within this period you can restore back to inbox but if it is more than after 30 days it automatically get deleted from trash folder ,and this video show you how to restore all permanently deleted emails in gmail

Link:
https://support.google.com/mail/contact/missingemails