Java - Allow one thread in a method without waiting

I've a situation where I need to implement a thread safe method, The method must be executed by only one thread at a time, And while the method is being executed by a thread, all other threads trying to execute the same method shouldn't wait and must exit the method.

Synchronization won't help here since threads will be waiting to execute the method sequentially.

I thought I would achieve this by making use of ConcurrentHashMap using below code, but not sure if this is the perfect way to implement it.

Class Test {

private ConcurrentHashMap<String, Object> map = new ConcurrentHashMap<>();

    public void execute() {
        
        if (map.putIfApsent("key", new Object()) != null) { // map has value for key which means a thread has already entered.
            return; // early exit
        }
        
        threadSafeMethod();
        map.remove("key");
    }
    
    private void threadSafeMethod() {
        // my code
    }
}

You can do this without synchronization, with compare-and-swap using a boolean:

private AtomicBoolean entered = new AtomicBoolean(false);

public void execute() {
   if(entered.compareAndSet(false,true) {
      try {
         method()
      } finally {
         entered.set(false)
      }
   }
}