The ideal solution would be to get Teachable to support DiscourseConnect in a similar way to what Memberful have done: Integrate Discourse with Memberful | Memberful.com. This is something that would need to be implemented by Teachable. It might be worth asking them about it though. They could probably get some assistance setting up the integration from the Discourse team, or from the Meta community.
For now, I think the best you can do is to use Teachable webhooks to trigger a Discourse invite email when a new user signs up on Teachable. There are some details about that here: What can the Teachable webhook do? - #3 by RGJ
Note that the approach suggested in that post can also be used on sites that are not hosted by Communiteq. This is done by pointing the Teachable webhook to Zapier (or a similar service) and having Zapier trigger sending the Discourse invite email. Details about configuring that on Zapier are here: Automate sending Discourse invite emails with Zapier.