What is the cheapest way to get CI for a Qt project?
One of the major advantage of the container technology is standardisation: easily replicating the same environment wherever a specific container is used, be it, for example, on your own machine during development or on the CI machine during the execution of the CI/CD pipeline.

Building and using custom containers is a pretty standard way of including OS-level dependencies (like libraries and toolsets, for example) which aren't included in a service provider's default container images. Depending on the provider the choices for the base image you'd use might be limited.

If you have a CI/CD provider which accepts custom-built containers (not all of them do, at least not yet) and you can meet their custom container restrictions (if any) then building the custom container for your case is IMHO a valuable investment. Not only for the CI execution, but even for developing of your app and ultimately for showcasing the container technology as a development technology itself :)