For one you could have a function that calls auth.run() and returns an empty doc and insert that as a client-side control. For reference see a similar GitHub issue.

This is a common scenario indeed. If your sitelet is based on a template, you can either modify the instantiation logic to plug your function, either into an existing placeholder or a new one; or just hardcode the call into the template itself within a <script> block.

Alternatively, you can require a custom server-side dependency (see the recent blog entry) that outputs the same <script> logic.