Could there be a new financial system not dependent on USD?
Yes, it is possible and there are discussions going on in many parts of the world about it to create a multi-currency system that is not solely dependent on pre-dominated US dollar-based system, and digital currencies such as Bitcoin is also an option. The major economic powers such as China and Russia are already using their national currencies to trade goods and services. However, completely moving away from US dollar poses significant challenges due to complexities involved and need for agreements among nations to establish and accept a new system.
The idea of a dollar-free financial system is just the beginning, it is difficult to say whether they will succeed or not. And honestly, I doubt the success of these ideas, but that doesn't mean the dollar will rule forever. Maybe this revolution of China and Russia will not succeed soon, but there will certainly be another revolution in the future, and the dollar will be replaced or eliminated it is only a matter of time. Because the history of mankind has proven, there is no powerful empire that has not been replaced over time.