When baby’s first teeth are coming through, a wipe with a clean towel is as good a way as any to keep them healthy. Once the child is old enough to brush, use a special children’s toothpaste. A small child tends to swallow toothpaste, and yours contains fluoride – fine if you’re spitting it out, but not if it’s becoming a major part of your diet!
Once the child has learnt how to spit out the toothpaste rather than swallow it, then adult toothpaste is fine.