Accidently deleted all my gmail emails from my mac mail account....is there hope for recovery?

To attempt email recovery from Time Machine backups, connect the backup disk to your MacBook Air and open the Time Machine application. Navigate to the Mail folder within the Library directory in your user folder, using Time Machine to locate data from before the emails were deleted. Select the Mail folder and restore it, being careful not to overwrite current Mail data. After restoring, open the Mail application to view the recovered emails; if not visible, manually import them. Finally, ensure the emails sync back to your Gmail account for accessibility across devices.