After reading the README, perhaps the next logical place to look is the build file(s).
Compile and Test
Maybe the Readme file did lay out how the code should be built. Even if it did, it may be useful to still dig into the build files. These can help show you how the code is laid out.
While it is generally not a requirement to understand how the code is packages, this can help give you hints about the code. It can tell you if the code is a monolith, or a distributed system. This will have the most up-to-date information on versions of components. Oh, the Readme called out Java 7, but the Gradle file actually uses Java 8.
CI/CD
It is becoming common practice to also put the CI/CD job descriptors in with the code itself. These specialized script files will show you how you really should be building the code, regardless of what the Readme might say. They will also show you the auxiliary steps that are run on the code, such as static code analysis or container packaging.
If the CI/CD jobs are not scripted in the code repo, it is useful to search them out and look at what they do.
Dockerfile
Dockerfiles and other container descriptors, or Kubernetes deployment files, are also great things to explore. These can show you how the code is actually designed to run. You may need to be cautious with these though. They may simply describe how some devs have set things up to run locally. The production deployments may not have anything to do with Docker or Kubernetes.