Now, and for the next few months, separation anxiety is at its peak. Although it's normal now for a baby to show an extreme attachment to you and fear of everyone else, it can be difficult for doting grandparents and caregivers. You can help ease transitions for your baby by warning people to approach slowly and let your baby make the first move. If your baby uses a thumb or pacifier to soothe himself as he tries to cope with his anxiety, that's okay. Sucking is one of your baby's only methods of calming himself.