Sim800l Project help?

Hello I have a Sim 800L Gsm module bought from ebay Click here. and I looked around it says 3.7v to 4.2v and 2amps Power supply needed. So used a straight 18650 battery and I'm able to power it up correctly because it is a 3.7v 2600mah battery. But i was thinking of making a portable project using a double AA battery on it with a Boost converter. problem is the booster i have only boosted it up to 3.3v and 500ma output. From 1.5v Double AA battery. They work great on my other portable projects but I'm not sure if it will work on mine. I could use some help. The project box i have to fit all this can only fit a double AA battery on it nothing more a single one.

The Sim800L module says 2amps But i have used 5v in down to 3.7v out and 500ma LDO converter i was able to send text messages with no problem. So my question is Why 2amps for?