Does .com.au rank better than .com in australia?

I have been looking to start a business for quite a while (5+ years), and have been sitting on the .com.au + trademark for a while.

During this time the owner of the .com domain has gotten a high domain score (71) and has become a big company in America.

When I search them in Australia Google it comes up with all sorts of information like there domain, Wikipedia, apps and socials.

My company will only be launched in Australia only, will I have a chance to come up first in the search results in my own country with the .com.au?