How do you continuously add characters to a story that originally started with a small cast? Is there a way to do this organically while making sure their presence in the story feels natural and not forced? Is it something that needs to be inside the beat sheet when you plan out the story? Because there are a lot of characters introduced, and my beat sheet doesn't cover any character, so it's hard to plan out in advance and making sure that their presence is both natural and not forced. Also, I don't understand what "forced" means and what are the criteria for their presence to feel forced.
To address your final comment first:
I don't understand what "forced" means and what are the criteria for their presence to feel forced
You don't want your audience to feel like they should have known about the new character before they appeared. For example, if your initial cast of characters includes two brothers, and you show many scenes of their childhood together, it may feel "forced" to introduce a third brother later on. In this case, the audience would feel like the third brother was added as an after-thought.
There are many ways to do this well, but many stories seem to broaden the story as they add new characters. If the narrative leads your characters to new places, it is natural that they will meet new people.