Congratulations! How wonderful you are to try to figure this out!
Your baby is telling you when he is hungry. He isn't ready to be on a schedule yet, and this early is too early for the 3 meal a day plan. This is the part of parenting that is exhausting. Nap when he naps. Freeze meals ahead of time for yourselves so you can warm them up and relax with your baby.
You'll get all kinds of advice, but waiting this out is the best way to go. Just give him what he needs. His tummy isn't that big, and may actually be having a problem processing the formula.
Does he have other symptoms? Is he waking up gassy? Is he waking up simply hungry? Is he waking up simply wanting to cuddle? It's hard but all those things need to be met!
A baby knows when it needs to eat. Your son duly informing you. :)
On a different part of your note: If your son is not gaining weight - or goes down to eating tiny portions altogether day and night, you might be asked to wake the baby to eat.
There may be an underlying problem (soy, milk, gluten sensitivity (and yes, you can have a gluten sensitivity to milk!)) that is stopping him from eating so much in one shot (There isn't much room in the stomach (about the size of a marble shooter at that age because breastmilk is made to go right on through; formula needs a little extra work).
Contact your pediatrician by all means - and keep an open mind - your son may simply be needing more than just food - attention might be the reason too. Babies thrive on attention - and gain weight too!
A lot more stuff if you have questions - just email.