Hi There. I am Bing and I look forward to helping you with your issue today.
If you access the emails using proper protocol say IMAP, all emails should be still there on the server, except you did delete the server side emails.
Normally, if you did nothing after just deleted all emails in your Inbox, the emails should go to the Trash and stay there by default for 30 days before physically deleted. You still have time to save them. Just log in your Gmail box, then go to the Trash folder, see if they are still there!
Any update please?
Any feedback about your email recovery please?