What do you want to use the brushless motor for?
You need a pwm output to control the ESC, and you might not have that on your stepper control card.
If you have an Arduino board you can experiment generating a pwm signal and run the brushless motor. The pwm signal goes to the white wire and grd goes to the black. The battery (or dc power supply) for the ESC goes between black and red. That would be +5v to the red from an arduino. This is a good idea to help you learn how this stuff works.
Observe voltage limit of the brushless motor, sometimes listed as 3S, 4S etc. This refers to the size (number of stacked cells) of LiPo batteries. The current draw of an ESC is quite large compared to common power supplies capability, so using a brushless motor in place of a stepper is a bad idea. Typical ESC might be 40A, and go up to 160A and higher. I have a water cooled brushless motor that uses 4S batteries and a 200A ESC for an RC boat. A stepper motor might draw 3A.
A brushless motor and a stepper motor are very different with different intended use. A brushless motor is a 3 phase motor, like a blower motor, so using it as the spindle motor of a cnc machine is it's only choice, and a bad one. They work very well spinning a propeller on a quad-copter due to large power developed and variable speed, and the ability to use a battery.
Stepper motors are not intended for fast, continuous rotation like a spindle motor or a blower motor. They move to an exact position based on the number of steps ordered, usually 200 steps per revolution (or a multiple of that). This is why they are used to move the axes of a cnc machine ... precise positioning at a slow rate. A 24vdc 15A psu are enough for three of them, and way cheaper than batteries.
Learn how 3 phase motors work (the 3 leads circled in black above) and how radio controlled models are controlled (small plug circled in blue above).
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