You can move messages out of your trash if you deleted them in the last 30 days.
- Open Gmail.
- On the left side of the page, click More
Trash.
Archiving messages rather than deleting
If you want to clean up your inbox without deleting your emails, you can archive the emails. When you archive an email, it gets moved from your inbox to a label called "All Mail" and isn't deleted. If someone replies to a message you've archived, the message will come back to your inbox.
- Open Gmail.
- Open the message or check the box to the left of it. To archive multiple emails, check the box next to all emails you want to archive.
- Near the top of the page, click Archive
.
Tip: If keyboard shortcuts are turned on, you can also click y to archive an email you're looking at.
When you search in Gmail, your results will include any messages that have been archived.
<source: https://support.google.com/mail/answer/7401?hl=en&ref_topic=7065107>
<source: https://support.google.com/mail/answer/6576?co=GENIE.Platform%3DDesktop&hl=en>