How to time breastfeeding and pumping together?

I want to give my partner a break from breastfeeding by feeding our 3 week old baby pumped breast milk. But she can't seem to get a break to get some time to pump.

She picks up the breast pump and the baby starts squirming and getting hungry and then crying. So she starts to breastfeed.

Then the baby relaxes, but the boobs are empty so she can't pump.

After an hour she might be ready to pump but the baby wakes and wants more milk. Repeat over and over.

How the hell can we build up a supply of breast milk for me to use?

We are currently using formula for when my partner wants to sleep or needs a break. She can't pump when she's hallucinating with sleep deprivation. Obviously we'd prefer breast milk for this.

How do we do it?