No, though I did first try connecting the 5V output to a resistor/LED circuit to make sure it was conducting current. I didn't measure explicitly though how much current it was conducting though.

The converter I used was an LM2596 buck converter (https://www.amazon.com/gp/product/B008BHAV4Y/) which is supposed to be able to provide up to 3A.

I'm not sure what I did wrong here.

The Amazon page for the converter (https://www.amazon.com/gp/product/B008BHAV4Y/) does say this:

"Output: DC 1.5V to 35V voltage continuously adjustable, high-efficiency maximum output current of 3A."

Does it only give around 3A when on the high end of that voltage range?