Is it possible to connect an apple tv to a new wifi network if you don't have your apple tv remote?

Not really.

Replacement remotes can be had for less than $30 from Apple.

Hi. Got to App Store and download the Remote app. It's an app that makes your iPad or iPhone a remote for the Apple TV! I like it especially if you need to type a lot text.

The remote app requires it to be on the same network and home sharing to be enabled, so the physical remote would still be needed to set that up.