Using LM2596 step down with LiPo
First of all as per the datasheet of LM2596 needs minimum 4.5V as supply voltage. So I think it will not start to output 3.3V even though you connected a fully charged battery.

As you have mentioned in the question the capacity of the battery is 2.6Ah, for most of the lipo batteries they can output a maximum discharge current of about its own capacity, for your case it will be 2.6A, but the battery will not support to discharge at 1C for long time. You have to check and confirm it in datasheet of the battery. Even though the battery is discharging at 2.6A it is will be input of the LM2596 and there will be loss at the voltage regulator section depending on its efficiency. More over when the battery discharges the voltage starts to decline, which will also reduce the current. For better reliability you have to use much higher capacity battery like 3Ah.