Suppose that we have a Java application, rather than a library, which is available through Maven central. For example, one such project is jol, which has its corresponding CLI interface in Maven central.
As far as I can tell, the main difference from a library is that the corresponding JAR file contains a class with an appropriate main() method and, optionally, a related Main-Class: header in the JAR manifest. If such an artifact is used as a dependency on a project, Maven will happily download the JAR file to the local repository along with its dependencies, as it does for any other artifact.
Is it possible to use Maven to execute such an application directly, without setting up a Maven project?
The exec:java plugin works nicely for local projects by setting up the JVM classpath so that dependencies are available. The user does not have to worry about JAR or .class file locations and such. Unfortunately, from what I can tell, it also requires an enclosing Maven project, so it cannot be used from an arbitrary command line prompt.
No, Maven will not do what you are asking for. It is a build tool, intended to build a Java project based on it's pom.xml file which describes the project.
So, you can't run a maven build without a pom.xml file. And if you have a pom.xml, then by definition, you have 'set up a Maven project'.
As @DaveNewton says, you should be able to set up a very small pom.xml with the dependency for the jar file in question, and the exec-maven plugin. I'm afraid that it's just not going to get any simpler than that.