No problem!
That is what Gmail's Archive function is for. Archive will file all selected emails, removing them from your inbox. Archived emails are stored with the label All Mail so they can still be accessed if needed.
Here's how...
For this example, I will archive everything older than 30 days.
1. Type the following into your email search field: in:inbox before:YYYY/MM/DD
2. Click the check box at the top of the email list to select all as shown below.
3. Click on the link that says "Select all messages that match this search" so as to include ALL documents, even ones you can't see on later pages.
4. Now simply click the Archive button as shown below.
You're done!
Remember, you can locate your archived email messages by using the search feature or by browsing the label All Mail.
