Do all babies get sick the first few days of preschool? How long does it take for their immunity to build up?

Yes, it is quite normal for kids to fall sick during initial days in school as the virus in the cc spread easily. Normally after 2 to 3 months it will get better and kids' immune will be stronger. For me I do not fancy giving supplements. I normally give wholesome food in vegetables and fruits to build up immune, especially those are high in anti-oxidant.