Thank you for posting your picture. It seems like you are supplying only one pulse to the step pin, which would result in the motor taking only one step. More information on the step input can be found in the Functional Description section of the A4988 datasheet.
If that does not solve the problem, could you tell me more about your setup? What are you using to supply power? What is the current rating of your stepper motor? Could you please post pictures of your setup with all of your connections clearly visible? Could you also post a picture that clearly shows your soldering joints?
The white cable is 5V ground
The Yellow cable is the step
The red cable two supreme is 5V positive pole
The green cable lowermost is the 24V positive pole
The bluw cable seccond bottom ist the 24V ground
Thank you for posting the additional pictures. It is still unclear to me how your driver is connected to everything else in your setup; could you post a schematic of your entire setup? What are you using to produce the signal shown in your final picture? Have you verified that it is producing the signal you expect? It is hard to see the soldering joints in your pictures, but it looks like they could easily short together. In general, if you want to solder wires to your board, I recommend soldering them directly to the board rather than the header pins. However, since they are already soldered to the header pins, I suggest using electrical tape or heat shrink around the soldered pins to protect against shorts. I noticed there is an “X” marked across your 24V supply; have you measured all of your power supply outputs with an oscilloscope or multimeter to check that they are what you expect?