You are never too early to start reading. When my son was under one, I already started reading very simple one-word picture books with him. I even just left some books randomly around the house to encourage him to pick them up and flip through them. Bedtime stories were something I implemented once he showed signs of understanding our conversations. And I truly believe that it was because I introduced reading at such a young age that he enjoys books today.
If you’re afraid that your child may be too young, I would suggest that you at least start introducing your child to books when they are a toddler so that they would be attentive when others read books to them like at daycares or in school. When you introduce reading at a young age, they would naturally become excited about storytime. Being able to capture a child’s attention through a book is a very important step for success in the future.