"only that the resulting DB matches what is expected"
So you need to take some fixed sets of test data, run the ETL process and compare the content of the resulting DB with a set of reference data. That's it. The test data sets should be small enough to let you verify the result in a reasonable amount of time, and complex enough to cover all important steps of the ETL process.
How you do the comparison technically is up to you, it depends on the specific database system, the availability and size of the reference data, the overall size and complexity of your system, the tools you have at hand to make a meaningful comparison, your time constraints, the required level of detail of the comparison, your personal skill level, and so on. There is no "one-size-fits-all" solution to this, you need to find out what suits your needs best and taylor your environment to this.