Yes, I'm sure they drank their mother's milk, that's what mammaries are there for. It's not the same as eating meat, if you are breastfed you aren't eating your mom for dinner!
I dont recall an explanation of what baby goats were fed in the garden of eden. Did I miss something in your question or about the garden of eden? Did they have baby goats then or were there only dinosaurs. Or maybe the baby goats ate milk weed. This is truly a perplexing question deserving much meditation.