Cluster feeding

Our son is only six days old but has now been cluster feeding for five days. It starts around 10 pm and goes until 4 or 5 am nonstop. There is zero break in between breasts. We do not get any relief time to even put him down for a quick power nap. He is perfect during the day but nights he’s inconsolable. My husband has to go back to work in two days and there’s no way we can function much longer with this pattern let alone him try to be functional at work. Any advice?

Background: my milk has come in, he’s latching fine. He’s not just hanging out when he’s on my breast but actually feeding.