WhyUhaveToBeMad said:
I really think that the art is smth that reflect reality and help people to be fulfilled world and first of all themselfs becouse world is first of all people living in it .I think that games are one of the best supplier of emotions if we are talking of art, because it game-play wwith a link with story make really strong connections with character and world around so i want to make games that will have this strong connection but that will bring my ideas and vision of the world. I want to know the way how to make this connections and discuss with someone this ways and ideas about game design and games in general.

It depends on genre and every game in detail, but a common way to build it up is like this:

The player first gets familiar with basic controls and interactions. For example, you can navigate freely in a 3D world, open doors and go to another room.

The games story may then start early, e.g. with establishing association to the protagonist. I remember Stray, the cat game, as a recent example. The game starts. You can control a cat. There are other NPC cats. You can interact with them socially. Then an accident happens and your cat falls down a hole, and finds itself disconnected from it's friends in an unknown underground world.
That's a very good start, because it does many things: The interaction with your cat friends (hugging, playing, having fun) makes it easy to associate with the cat protagonist, because the cat is nice and has a good time. After the accident it is clear what you want to do: You want to get back to your cat friends to have a good time again. You don't want to be lonely and lost in the underground. So the player is motivated, and thus interested of what comes next, and willing to solve some problems to achieve the goal.

But there are many very bad examples too. E.g. part X of some never ending game franchise. Those games often forget about building up association with the protagonist, and they also miss to build up motivation. The games start with the assumption the player already ‘knows’ those things from the former titles. However, this is not about knowledge, it is about emotion, which has to build up first no matter what. The result of this failure, to me as a player, is that i feel thrown into a world of which i do not care about. And i have to kill dozens of ‘bad guys’, although i do not know why they are bad at all. So i'm not motivated to kill them, or to play the game. I'm bored after 5 minutes and refund the game.

There are also many examples of the other extreme: Too much story right at the start. Examples are Sonys games. I've tried HZD or GoW. Those games start with teeny and cheesy cliches. Reprises about childhood of the character, or the problems of raising a son. The execution is great. I can see they really are good at imitating Hollywood, but the problem: They do all this before letting me play, connecting to the world, and see if i like the gameplay or not. So after watching boring movie clips for half an hour, i have to refund the game before i even played it, simply because it feels like i'll probably don't like it, judging from the lowbrow story tropes i've seen so far.

So in my opinion, even if telling a story is your main goal, the game is always more important, and should be introduced first. Only after i am an active part of the games world and motivated to play, i am interested and ready to be introduced to story, lore, etc. Story has to come slowly and gently, so it does not terminate my existence in the games world. If you interrupt my playing with never ending cutscenes or walls of text, i do no longer play the game. Instead i become a passive consumer, just like with watching movies or reading books. It's just that movies and books are way better with telling stories than games can ever be, because as a storyteller, you can not integrate an unknown player, acting unpredictable and at free will, into your story (mainly about this unknown) at all. Thus, storytelling in games is very limited and can only work if we respect those limitations. The deeper your story is, the more you have to force the player on taking the role you want him to be. That's no bad thing, but it's hard to force and manipulate some stranger into some role without him to notice he's forced and has no choice. But that's what we have to do. We give players the promise ‘You can do what you want in my game. Your choices matter. There are multiple endings. etc.’, but this promise is an intended lie. In fact we manipulate the player to do and experience what we want, and the art is to do this so gently nobody realises. Because our medium is interactive, that's much harder for us than for authors of static content.

The related strength of games isn't storytelling, but mood and atmosphere. We can do this much better than movies or books, because we can deliver immersion and interaction.
To me the priority goes: Mechanics > atmosphere > story. If a former thing fails, a latter can't get it right even if done perfectly well.
Thus, it's no good idea to begin the design of a game with story, characters, background, lore, etc. The first thing is to make a proper gameplay loop which is fun (or some other emotion you aim for), and then see which kind of background fits.

But that's just me and my personal opinion. I did not read this in a game design book or something like that. ; )