He is so young.
They don't have regular sleep yet.
Sleep patterns are not static in a baby or child.
It changes per development, per teething, per hunger, per hitting milestones, per hitting growth-spurts.
Him waking at 4:30, is to me, good.
My kids as babies, woke every 2-3 hours. I nursed.
How come, your Doc said not to give him bottles?
If a baby is hungry, they are hungry.
Both my kids as babies, had GINORMOUS appetites. Especially at growth-spurts.
Going all night, with an empty tummy, is hard.
Why not, just feed him and give him a bottle?
Our Pediatrician said, for the 1st year of life, a baby's primary source of nutrition and calories, is from breastmilk or Formula. Not solids and not other liquids. And to feed on-demand. Day and night.
They are growing so much and this is a building block period for development and growth.
9 moths old, was a growth-spurt time. IF for example, a baby's intake is not keeping UP with the baby, they will be hungry. A baby grows and needs more frequent feedings, per growth-spurts. If not, they are hungry. For example.
Suppose your baby, goes to bed at 7:30pm. (I am just assuming since you did not say when he goes to bed). That means, that from 7:30pm until he wakes at 4:30am... he has slept for 9 hours straight. That is a LONG time, for a baby. And his tummy is empty.
"Sleeping through the night" for a baby, means, sleeping at least in 5-6 hour stretches.
Your baby, IS doing that.
Your baby, IS sleeping, well.
To me, just give him a feeding and his bottle.
Go by your baby's cues for hunger and needs.
Not by the Doc saying no bottles anymore.
Our Pediatrician, is the opposite.
A baby, does not have to wake up in the morning, at that same time as an adult. MANY babies/kids, wake at 6:30am. Mine do as well as ALL of my friends babies and kids.
This is a common time, for babies to wake. And even older kids.
Kids wake early.
For me, 6:30 is the norm and not early. Because, I am awake already.
I don't make my kids sleep later, if their natural clock, is them waking at 6:30am. That is just them.
Kids and babies, do not start waking up later in the morning, until they are Teenagers. Then, Teens sleep in until late.
Babies/kids/teens and Adults, simply do NOT all wake up at the same time in the morning.
Childhood.
I would go by your baby's cues for hunger and what he needs. Not what the Doc says about no bottles anymore.
Also, let your baby have a Lovey in his crib.
My son from 6 months old, had a lovey.
He'd rub it and that soothed him.
And, I had a couple of other baby safe stuffed toys in his crib too. Even if he waked, he'd be playing in the crib by himself for a bit. Until he then "called" for me. I KNEW his sounds and his cries, and whether it meant he was playing or needing me or was hungry. And many times, my son would just be babbling to himself and making noises... in his crib even if awake. But he was fine. He "played" in there and would call for me when he was ready. Or he'd have this rhythmic sort of 'cry'.... but I knew him and knew this was his tired cry and then he'd fall back asleep. If not, I KNEW he was hungry. So I nursed him.
Hunger in a baby, also varies. Daily and nightly. You can't always schedule it. If hungry, I just nursed my kids. I knew they were hungry.
Just let your baby wake, when he wakes. At that 6-6:30am time.
Why make him sleep longer, just to get him to CIO longer or to make it a point of it?
To me, your baby is waking per his natural waking up time.
When he wakes at 4:30, just feed him.
He's hungry. Then he will probably go back to sleep.