Yes it is possible to create a new system that is not dependent on the USD. In fact, there are already alternative systems in place, such as cryptocurrencies and bartering systems. Cryptocurrencies, such as bitcoin and ethereum are decentralized digital currencies that operate independently of governments and traditional financial institutions. They allow for peer to peer transactions without the need for intermediaries such as banks. Bartering system involve exchanging of goods and services directly without the use of money This type of system has been used for centuries and is still used today in some communities. It is important to note that the USD is currently the dominant currency in the global economy and any new system would face significant challenges in gaining widespread adoption.
Well, in theory, a new financial system not based on the dollar could exist. But the currency of such a financial system must have the same liquidity as the dollar, that is, it must be freely bought, sold and exchanged in almost all countries of the world. It would also be good if such a currency were not the national currency of any state so that such a state would no longer dominate the financial market in the world, like the United States now.
Theoretically, this system can be achieved on a small scale. This means that a country can cut off all its economic ties abroad and establish either a financial system that relies for its resources on its own capabilities only, or establish a system that depends on external connections in currencies other than the dollar. The second possibility would assume that this system would never be worth buying products in dollars, which is a little difficult, if not impossible, in a global economy that depends on the dollar.
As for the second hypothesis, which is the establishment of a global system without the dollar, this is theoretically possible, but almost impossible in practice. The dollar did not reach this position overnight, and that required decades of development accompanied by developments in the global economy.