Arduino and AWS

Hi everyone

So I am trying to find a way to connect an arduino with a 3g module attached, to aws or rather the aws api gateway.

It's proving difficult as I know the arduino yun has some sdk support but I want a cheaper option using a standard arduino mega with a 3g module(I was considering using an esp8226 but I would have needed to connect to enterprise networks which I know is a problem in itself right now.

Is there any way at all that I can connect it or send requests?

The protocols I know it supports are mqtt, http and mqtt/http via websockets

My plan was arduino->api gateway->lambda->dynamodb

Thanks in advance