can I transfer files from old Mac to new iMac without wifi? ...using thunderbolt only.

Please help us help you. The exact sub-model and the macOS version of the "old Mac" is important; port types and transfer protocol compatibility have changed over the years. Examples: Mac made before 1998 do not have USB ports. Macs built before about 2011 do not have ThunderBolt ports

Thank you.

A 2010 has wifi built-in and shipped with macOS 10.7. The last Mac notebooks where WiFi was an option were introduced in ~2003. You can turn on the wifi in System Preferences. Still, wireless amy not ebteh besst way even if everything works.

Moving apps makes no sense because those on an older Macbook Pro are not going to meet the 64-bit requirement of macOS Ventura. Data files—text and WP docs; photos, spreadsheets; etc—can be moved as they are more likely to be compatible with newer OS versions. But wifi may not be the best, fastest, or most reliable way

What I do when there is a great difference in computer ages is to use either a USB thumb drive or an external USB hard drive as a transfer drive. As the new iMac has only USB-C ports, you'll need an adapter like this one.

Before starting, I make certain all files needing a move are in ONE folder on the old Mac. Then I move that folder to the transfer drive and connect the transfer drive to the new computer and copy the entire folder to the new computer's desktop. Then one can leisurely go through the files and test to see which will work.