You can introduce hay from day one, although I usually wait till they are at least 4-7 days old. At that age it does not need to be good quality nutritious feed, just clean straw to get their rumen working. The good quality hay should be introduced in time for them to be eating hay well by the time they are weaned off milk.
Our calves start tasting hay within the first couple days. We keep them on the cow for a few months, so they like to try whatever mom is eating. I separate the cow/calf overnight and usually give the calf a bit of hay in case she wants to eat some overnight.