Hi SummerGAL,
Welcome to the 
Wrap Club! You did it! Yay!!!!!
I wonder if your hunger is real, or if it's a mixed up signal to your brain. Generally most people aren't bothered by hunger this soon. I have heard of it rarely, though.
Often people feel full after a very small amount of food because the top of the stomach is swollen and the brain interprets that as fullness.
I'll bet it subsides soon. I can tell you this. I don't know what your surgeon will advise you, but I was able to chew, which is key, my own food. As long as it could be chewed to a liquid (creamy consistency) I could eat it.
It was much more satisfying than a liquid diet with no chewing. Just knowing you can make choices is good. During the first couple weeks I stuck to soups or soft foods, but saltines chew to a liquid easily.
If your body is one that doesn't feel full after a quarter to a third of a cup in the beginning, you'll have to be the eating police. Just because you can eat more than that in the beginning, doesn't mean you should. People whose stomaches don't stop them from overeating with fullness, can get into painful situations by overeating. I don't know if this will be the case for you, but just keep it in mind.
Hang in there. The next two weeks are the most challenging. Keep in mind that your wrap will start swelling and peak at around the two week mark. Because of this your swallowing will get worse before it gets better.
You're lucky that you had a few burps...it means you'll have far less trouble with painful bloating, and that's great!
Happy Healing!
Denise