My baby is 6 month old (8.4 kg). He has a fancy play gym with plenty of lots of toys. We also have plenty of books to read to him. We make him play with our dog (poor doggy!). He also loves playing with leaves outside while we hold him in our arms.
Baby playing in the early morning
In the morning, in the first hour of awake time, just before his first nap, he is generally quite able to play on his own. He can turn on his side to catch toys and play with them. When I try to interact with him, he mainly shows interest in his toys.
He is not very good at turning from his tummy to his back yet (he is usually in "airplane mode" when on his tummy) and he sometimes complained to be turned back on his back. During tummy time, he is sometimes playing with whatever toy we put in between his arms (or some other toy that is nearby at the moment he flips over on his tummy). He sometimes looks at himself in a small mirror that is by the side of his play gym or just looks around a little bit. Often, he goes airplane mode and starts fussing though.
Baby playing during the rest of the day
During the rest of the day, however, things are very different. He refuses to play on his own. He does not really try to reach for toys, he accepts when we put one in his hands but starts fussing just 5-10 seconds later. During the whole day, we either directly play with him, often read him stories, walk him outside to allow him to grab leaves and things. If we play in a given position (say, sitting together in our bed), then he is good to play for about 15 minutes and then he needs to change activity. He refuses to be lying down and he does not enjoy to be in the carrier if he cannot reach for things to play with.
I would tend to think that his fussing behaviour is unrelated to the developmental of object permanence as he complains just as much if we are present but don't actively do things with him.
In the morning, he typically is with me and during the day, he is with my wife (hence she gets most of the fussing). When I am present during the day (I stay at home about 4 days a week), he fusses just as much as when he is only with my wife. I am unsure as to whether our behaviour affects our son's envy to play on his own and whether we can do anything to make our son more at ease with playing on his own.
Can we encourage our son to play on his own? How can we do that?