I can't know what the problem is but here are at least a few potential reasons based on looking at your circuit.
You are connecting a 5V MCU to a 3.3V chip. If your MCU expects any kind of response back from the chip, 3.3V signal may not be high enough for the 5V MCU to see it. Powering the circuit with a separate 5V supply is a worse scenario because it powers the 5V MCU directly, the USB scenario is a bit less worse because it powers the MCU via a diode which makes the MCU voltage lower and it can detect the 3.3V signal because it's in the guaranteed operation limits.
One option is that there is too much capacitance. You have 200uF for some unknown purpose. It may take too long to charge and voltage rises slowly, so the MCU starts up before it has enough voltage to run at the speed required and it executes garbage. Since the 5V supply can provide 7A it may not be the issue.
But you have a 7A switch mode power supply and it should be able to charge up the 200uF quite rapidly at start. The next problem might be that it's a switch mode power supply with extremely light load compared to the 7A rating. It may have too much switching ripple and noise.
And you also did not disclose how you connected the power supply to mains, as you needed to do that yourself. It must be wired to a three prong plug with earth, for safety and the mains filtering to be functional. And it must be connected to an earthed mains receptacle too. Without earth, the supply output will have common mode noise at mains frequency and at the switching frequency.