I couldn't find any direct examples on how to programmatically configure a datasource with Quarkus in the docs, only a reference to TenantConnectionResolver and a GitHub issue asking about it. Armed with these helpful, albeit vague tips, I figured out how to do it and made this example app to demonstrate it.
Every time a request is made to the /test endpoint, the app generates a new H2 database and inserts a TestEntity into it.
The Quarkus docs and terminology refer to this capability in the context of multi-tenancy, which makes sense. However, being able to programmatically create/resolve datasources is conceivably useful for other purposes as well. For example, the whole reason I started researching how to do this was because I wanted to create an app which used sqlite as a datasource, and the sqlite file itself could be located in multiple places.
I have tried to annotate the respective configuration and code with comments for specific details of why that code or configuration is necessary. If you still have questions after reading through them, feel free to open up an issue and I will attempt to help clarify any confusing parts.