Yes, you will need to be connected to the Internet in order to sign in or create your Intuit account as part of activating your installed software. Please see this help article for more information.
See here for information on how to contact TurboTax Support if necessary.
FWIW check here for Mac specific troubleshooting but some of the advice is a bit basic
some folks reporting this type of error the past couple of weeks on Mac OS 15.2 Sequoia were finding that it wasn't an internet connectivity issue per se, but some problem related to keychain/passwords from old versions and were eventually able to get it working by installing in a separate user account on the same Mac (which is not ideal).
Not sure what your situation is but this internet connection error doesn't always seem to be an issue connecting to the internet. As another example, loading a garbage file as my 2023 return instead of the .tax2023 file returns an error obviously, but says "we recommend you check your internet connection and try again".
Anyway, try the troubleshooting, if still stuck you might want to try calling Turbotax.
fyi this was the earlier thread on this topic (which also coincided with an actual connectivity issue on the TT side but that cleared and some folks still had issues)