Is it normal for my baby to get sick from other kids in daycare?

Yes. For the first 6 months of daycare, children do tend to catch many colds. It's inevitable and yes, a normal part of being in daycare. It is merely a function of being exposed to many other children who will unknowingly spread viruses before they become sick themselves. Be proactive by making sure your baby is eating and sleeping well and is up to date on all his immunizations.
Yes. The sad reality is that illnesses are ofter contageous before the first signs are present. Adults may possess enough immunity to acquire & pass viruses and never feel sick, so the kids & adults at day care may spread illnesses. Pregnancy passes temporary immunity to many illnesses, but this is gone by 3-4mo. So older infants in a close nit setting will share new germs as they come along.