Unsure if babies can form memories ages 1-2, my oldest memory is from around age 3. They do learn words when they are around 1 year old, so there must be some capacity for memory? What is going on there?
Of course they have memory, how would they learn otherwise?
Forming actual memories of situations and people comes a bit later, though. Still, humans can be traumatized at any age, even a baby that can't form conscious thoughts yet.