Speaking as a mathematics professor -- In my opinion, it's like asking "Can I become a concert pianist without taking piano lessons?" Well, sure; indeed, it's

Speaking as a mathematics professor -- In my opinion, it's like asking "Can I become a concert pianist without taking piano lessons?" Well, sure; indeed, it's been done before. But if you're going to put in the hard work, why not enroll in a Ph.D. program? They're designed precisely to train you to become an effective researcher. And they often offer funding. Earning a PhD is hard. Becoming a strong researcher outside of a PhD program is even harder. If you want to put in the necessary effort, then absent unusual circumstances I'd recommend earning a PhD. All sorts of infrastructure is in place to help you succeed.