in my experience, most babies are born relatively pale. Most of my patients are Hispanic, Native American and Caucasian, so this might not help your story much, but with a hat on the kid, it is hard to judge a baby's ethnicity between Caucasian and Hispanic. I can tell the difference between a Navajo baby and Pueblo babies though. : ) Many of my Hispanic families (and there is a wide range of origins and backgrounds for these families, some have been "here" for 400 years straight from Spain, others migrated from Mexico (with a mix of Spanish and/or indigenous backgrounds), or Central or South America)....anyway many of these familes comment on how "white" the baby appears at birth.
The babies with Asian backgrounds (generally Vietnamese, Korean, and Hmong in my location) or African (Sierra Leone) or African-American or babies whose parents have come from the Middle East generally have facial characteristics reflecting their ethnicity, though their skins are quite white at birth.
This is of course just based in my baby-catching experience and may not apply to babies in other parts of the US or of the world where the genetic backgrounds may be quite different.
If you need your baby to appear white at birth, many simply do if you regard their skin tones independently, but their facial features often reflect their heritage more accurately. The hair (or lack thereof) often hints at the parents' ethnicity, but most babies have hats on within minutes of birth (they are fashionable that way!).
Boy, if you need some stories in this regard (tension, accusation, tears and hysteria!) PM me.