Let me start by saying that I am not an expert and I am sure their inborn personality also plays a role on how well they play on their own, but I often get asked about how I got Sofia to play independently, so here goes my personal experience.
I truly started implementing independent play from a very early age. I have always been alone with Sofia all day, therefor, part of my schedule with her always included some independent play blocks (even if it was 15min), on purpose, to get her used to it. Usually while I cooked or got ready casually close to her, without being right in her face.
Slowly through the years, I have seen a huge development of that independent play, month after month, it got longer, and she keeps exploring it on her own, without it being "time". Which I love.
Here are my top tips of what I think helped.
Start young. It's never too late, but if you have tiny babies, make a conscious effort to get them on independent play time for a little every day. Usually at the same time, one that works best for their personality. For example, I always have her on independent play at home after big outings or after she wakes up, both times when she is more physically calm. And right now, she has a lot of independent play moments voluntarily through the day.
Engage with play time & undivided attention. As important as it is to block times of the day for independent play, it's also extremity important to block times to be fully connected only playing with them one-on-one. I found that, giving her exclusive attention during the day has made her super independent because she knows I am there for her.
Toys. Of course, having the right toys is key, especially those that are creative and can use their imagination & play role. Here are my favorite toys for the house.
Don't interrupt play time. Even if a diaper needs to be changed or food needs to be served, if she is playing longer, I let her play longer. The less distractions, the better & longer she learns to play.
Get to know their interests. Sofia loves princesses, dresses, makeup (things I never forced into her or showed her) as well as balls, scooters and bikes (again, something SHE asked for) so paying attention to those activities that she (on her own) is interested in, and providing some of those games & materials for her to use, also has helped in their independence, since she's then engaging in activities she truly has an interest for and helps her deep explore her likes.
Limit screen time. I really did not give her screen time until she was past two, and honestly, def increased with quarantine life due to the lack of social activities, however, the more screen time she has, the more she wants it, which takes from independent play time. So I limit it to a time a day.
Make a play space. We have a downstairs area where the living, dinning and kitchen is all together in one big space. So I love having her little play area corner there, as well as her toys (hidden in bins) so she can pull out and play, while I cook, clean, am sitting in the couch... having everything in one space makes her way more independent and willing to want to play, rather than have to go to her room and play and be on constant watch. We are all independent, but together, which she loves. It allows us to give her space, while also being "present" without being in her face.
Choose your battles. Sometimes playing independently means getting messy, or taking three baths/showers a day (again, quarantine life here). So hey, is that the end of the world? No. Unless it's a big mess/deal, I am okay with it.