No sleep?

Is anyone getting sleep at night? Baby is 4 weeks 5 days and we are going crazy. At the beginning of the night he’ll sleep. Last night he slept from 9pm to 1am. Then the fun started. Had a bottle at 1, but around 230 he was noisy in the bassinet. I had to pick him up and have him next to me till 330 (I was awake of course). Had another bottle then. We got a little break, then he started again with the noise in the bassinet. He doesn’t want to be in there. He wants to be cozy laying on one of our chests. And we are so desperate for sleep that we’ll do anything. Is anyone else having a similar experience?

The pediatrician says that it’s too early for a sleep pattern and too early to spoil him. But we are going nuts. Thoughts?