In short, no. In practice, you probably should. You can try to find a free lawyer through a legal aid office, but legal aid attorneys often have high caseloads and strict rules for what types of cases they can take. If they can take you on, great. But chances are they won’t be able to provide meaningful help to most people.
All other disability attorneys get paid the same and the amount they get is regulated by the federal government. They take 25% of your first check (capped at $7,200), if you win benefits. If you don’t win benefits, they get nothing. A good lawyer (and all Atticus lawyers) won't take anything upfront or ongoing.