How to find number of winding turns for a three phase induction motor
Here is a rough idea of how to proceed.

If you know the maximum flux density and the size of the air gap, you can calculate the air-gap flux per pole. That would allow you to calculate an approximate number of winding turns for each winding distribution alternative that you wish to consider. To get a more accurate number of winding turns, you would need to consider the length and reluctance of the magnetic circuit in the iron and the effects of the slot size and geometry on the magnetic circuit.

To calculate the wire size, you would calculate the maximum size would fit in the slots. Then calculate the stator copper loss. If the copper loss is too high, select a winding distribution that is more efficient. In order to calculate the copper loss, you need to know the full-load current. To calculate that, you need all of the design characteristics of the motor including stator and rotor resistance and leakage reactance, magnetizing reactance and iron loss.

You won't be able to determine how much copper loss is tolerable without knowing the wire temperature rating, the other losses and the heat transfer characteristics of the motor.

You probably need to consult a text book to find a more detailed explanation and formulae. A text might also have some useful empirical data.