Is it impossible/possible to derive a formula or sets of formulas that lead to winning chess games?

Why would it be a "set" of formulas. Chess is just one game. How many formulas do you need?

I'm not sure why it would have to be complicated either. Tic-Tac-Toe has a little over 255,000 games that can be played, but the formula for perfect play is trivial. Likewise, Connect Four has a very simple solution with 4,531,985,219,092 possible positions to deal with. And mind you, Connect Four was solved in 1988, 14 years after it was developed.

"At the time of the initial solutions for Connect Four, brute-force analysis was not deemed feasible given the game's complexity and the computer technology available at the time." - Wikipedia

There's no reason to think that chess is any different just because it hasn't been solved at this time. Nor is there any reason to believe that a computer is needed to solve it, or necessary to prove the solution is correct by going through all possibilities.

"It has not been proven to be impossible."

You can't "prove" that people will not be able to do something that definitely is possible. A solution does exist, we just don't have it yet.

"Humans have developed some amazingly complex algorithms, including the 5ESS switching system. This program was written by more than 5000 employees over the course of 20 years and has over 100 million lines of code."

That comes from wikipedia. The source was a paper that had this line:

"The development effort for 5ESS reached up to 5000 employees (less than 1500 at the moment), producing 100 million lines of code..."

At one point they had up to 5000 employees. This isn't the same as 5000 programmers working for 20 years. I'm sure they had other people doing stuff like hardware, secretarial work, managers to slow things down, and of course janitors.

You must have solved chess to know this.

Not mathematically, but practically. Ask any GM or chess statistician if they think chess is a draw.

Theoretically solved.  

Practically unnecessary to spend resources.

Billions of  computer games ( Stockfish vs Stockfish alone has 1.6 billions of recorded games). and billions of human games were already played.

There is no single game where one side win ( without a single mistake from opponent).

from a mathematical point of view it is almost trivial to build such a formula. Zermelo theorem is constructive(*). The big issue here is the size of this formula (which cannot exist physically on earth in the case of chess)...

(*) In the sense of so-called (they discard the physical size of the problem) constructive mathematics, which is what people using formal provers do. A two player finite "zero sum" perfect information game is basically a finite tree whose leaves are numbers (in chess, -1,0 and 1). In this post we call the depth of a leaf/node is maximum of its distance from a leaf (so every leaf has depth 0). nodes who can be reached from the root in an even (resp odd) number of steps are called "white" (resp black).

You define inductively node values as follow: leaves values are the numbers on it (step 0); for every node (let us call it "x"), when all the nodes immediately after it (they all have depth k-1 if x has depth k)have been given a value, then if x is white, its value is defined as the maximum value of the nodes directly after it, and if x is black, its value is defined as the minimum value of the nodes immediately after it.

The whole tree can be annotated with this method and a player who would have such annotated tree with it would be able to play in such a way that:

-if he's white (resp. black), the value of its position (i.e. current node)will always increase (decrease) or stagnate

It is also possible to enrich the tree with the information, in each node, of the shortest path to the end (with optimal play); so either player gets the optimal result in the minimal number of moves .