Most parents unwittingly infect their children with cavity-causing bacteria.
Dental caries (cavities) are now recognized as an infectious disease. They are caused by bacteria, mainly Streptococcus mutans and Lactobacillus. Babies are not born infected with these organisms. They acquire them from a colonized source, usually a parent. Free of these bacteria, your child could be regularly soothed to sleep with a lollipop with no dental consequences.
Transmission is through saliva. Kissing a baby on the lips, cleaning a dropped soother by putting it in your mouth, or sampling milk from a baby bottle can all transfer the bacteria to the child.
So should you make every effort to keep your child's mouth sterile? It's a good idea, but the infection control measures should extend to grandparents, daycare, friends and all other contacts. A plastic bubble might be easier.
Or you could resign yourself and invest in a little Dora toothbrush.