You can do that by enabling “Allow guest users without accounts to create topics and replies”
Steps:
Settings -> Forums -> “check to Allow guest users without accounts to create topics and replies”
But I warn you, doing that you may face spam problem. A lot of spams. I am doing SEO for a cleaning company website. In that website, developer left that function open. When I started working, It has more than 12k spam replies and topics. So, think again before doing that.
