We have an 8-year old Persian cat. We got him from a breeder and bought him home at about eight weeks. Buddy is very aloof and self-absorbed and not at all affectionate. The only time comes near us is when it’s time to fill his wet food dish at 1630. He knows when it’s time. Anything else just interferes with his Olympic sleeping.
8 weeks is way too young. Cats’ personalities don’t come out until 4-5 mos and range greatly from very affectionate to aloof and solitary. Persians as a whole are easygoing and tend to be in the middle but closer to the solitary side. They will play and socialize but will not necessarily seek out these interactions. Just like with people, it all depends on the individual cat - what it has inherited from its parents; from environmental influences, such as being taught by the mother, early experiences with humans etc.