As someone else already pointed out, a score of zero is truly a null value. It's not worse than a 300 in the same way zero degrees Fahrenheit is colder than 30 degrees.

I would recommend four or five credit cards. Why that many? Because right now you're a credit newbie--getting new accounts doesn't hit your average age of accounts because you're at zero now. 0/0 is the same as 0/4.

If you build positive inertia, then bumps down the road won't hit you nearly as hard. When you do get a new account, your average age of accounts won't take nearly as big a hit.