Most newborns lose all their hair within the first three/six months of life.
During pregnancy, some of the hormones will cross the placenta and circulate through your baby's body. Shortly after birth, these hormone levels start dropping. If your baby was born with lush hair, you'll notice they'll start losing it. The same happens to new mothers when their lush locks slowly disappear after birth. Then later you may see a lot of hair falling at once. This is due to telogen effluvium, the process by which hair is lost three to four months after a stressful event.
Don't panic when you find scattered baby hairs on their mattress or car seat. Newborn hair starts falling out during the second month, continuing until your baby reaches 6 months of age or so. If your baby spends most of their time on their back you may notice a larger bald patch on the back of their head.
Once the new hair comes in, you may notice it's a different shade than the original color, most often lighter. The texture will likely be different as well since newborn baby hair is usually very fine and fragile. As excited as you are about their new locks, refrain from styling your baby's hair or using any hair elastics until they're a bit older.