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Yes.
Well, you can basically collect all or almost all of the bronze characters, the chance is quite high.
Silver is more difficult. There are characters from the main quest, you get them just like that. There are characters that you can 100% get from Side Story. It's a bit more difficult, but overall it's easy. There are event characters – you need to get them during the event. This applies to Mikasa and Levao, for example, from my list, but there are many of them in general, each event – at least one new character. Well, and otherwise, yes, it's random... Silver drops regularly in Gatcha, but which one – you can't control.
Gold is not very easy to get, as you can see from my statistics. But it's possible. In this regard, it's like legendary characters in Heroes of Might and Magic.
In principle, you can get a character of your choice – but for this you need to save a lot of crystals. I'm saving up now, but for a new player it would be excruciating.