NICU won't feed newborn baby until breast milk?

Just went to visit my daughter in NICU (she was born about 8 hours ago) I asked the nurse what's my daughters feeding schedule and she said "typically it's every 2-3 hours, but we're not feeding her anything until you produce your milk." I'm shocked because I haven't even seen the lactation consultant yet, but luckily I was able to get my hands on a breast pump, and I've been trying to pump in my recovery room but nothing is coming out yet. My question is, do they really let babies starve until then? Not even feed them any supplement? I hear some moms don't produce until 3-4 days early. Especially when I had to be induced early at 35 weeks. 😔