Is there a balanced chess system where players of unknown skill can have an equal chance of winning? Is there a chess system where you can make players of differing skill levels compete against each other with an equal chance to win without using different chess variations?

This system should give good players and bad players a level playing field where both of them can win.
Yes.

The way I've done this in the past is to play a series of games with clocks starting with 10 minutes each on the clocks and then the rule for subsequent games that the winner of the previous game gets one minute less and the loser one minute more. This quickly stabilizes at a level where both players have good chances of winning.