I assume you’re referring to App Tracking Transparency, the feature which displays a prompt asking you whether you would like to allow an app to track you.
This wouldn’t be straightforward to bypass outside the App Store, provided app sandboxing is left intact (which I expect would be the case if the installation of non-App Store apps was allowed on iOS). An app would have to find a way to store a tracking ID such that other apps, including those from other developers, could also see it. I don’t think that this is possible/feasible under the iOS app sandbox. Even if you “sideload” (install) an app through Xcode today, the app is still subject to that sandbox.
Even if it is possible, such a cross-app tracking ID would be much less useful than the one iOS optionally provides because there exist numerous data brokers who will all want their own tracking ID, with their own little fragment of the user’s data. It wouldn’t be a universally shared ID which corresponds to all the user’s data, like iOS’s.