Volunteering for the job nobody wants is how people notice who actually shows up.

The unpleasant task is visible precisely because everyone is avoiding it. Taking it on tells people something about you that no amount of talking would, and it tends to be remembered long after the task itself is forgotten. There is also far less competition for the credit.

Look for the thing in your group that keeps getting deferred and pick it up without making a production of it. Do it properly rather than loudly. Once or twice is enough for people to know who you are.