I use Google Apps with Catch-all filter. Now since I am the only user at my domain, I want to send the E-Mail the from email@example.com without verifying each username since I own all of them and they are just catch all. Is their any way to do this?
Yes it is possible but you have to make it by creating each pseudo-email account of your domain as an alias through Admin Console. You cannot just simply type whatever pseudo-email (alias) account you want each time you want to reply with it without having set it up before.
First you create an alias
Admin Console > Users > Account > Aliases : Add an alias > firstname.lastname@example.org
Then you configure your Gmail to make use of the alias you created as a sender
Gmail Mailbox > Gear icon > Settings > Accounts > Send Mail as : Add another email address that you own
You put the name you want, you enter the alias you created (email@example.com), you tick the "Treat as an alias" box and you are ready to go.
Now you can select this alias as a sender when you compose or reply to an email. You can create limitless aliases since they are not real users where you have to purchase a seperate Google Apps subscription.