Well it's a little early . They need to be fed every 3 hours. At 3 months you can put some cereal in his bottle of the night so he sleeps longer. Ask your baby's doctor for advice
My one month old just recently started sleeping through the night. One night he was fussing for his bottle but I had just fed him an hour before that. Too much milk gives him heartburn. So I gave him my knuckle to chew on and he fell asleep. Didn't wake up at all that night until 7 the next morning. (He fell asleep around 1) so I got a whole six hours of sleep lol I guess for him, my knuckle distracted him. And he doesn't wake up fussing for his bottle either. He's actually kind of calm and I'm able to make his bottle without having to hear him cry or fuss. I guess it depends on the child because my first born didn't sleep through the night until he turned 3 months.
A 1 month old still needs to eat frequently and most likely will wake about every 3 hours to eat. Unfortunately like @andrewsmommy, said, they have to be ready. My breastfed 7mo old still wakes 2+ times every night to nurse ¯\_(ツ)_/¯
All babies are different. Most babies will sleep through when their ready and others just aren't ready. You can really make a baby sleep through the nightm Especially at 1 month.