Of course not. She's portraying what amounts to a new character, at least to non-comic fans, so she lacks a foundation for the audience to build on.
That was true of RDJ in the first Iron Man - but there was no MCU for him to carry, then. Only once several of the heroes were established was there an MCU, and by then RDJ and Chris Evans had proven themselves capable of bearing the burden.
Captain Marvel the character might have the chops, but as it stands there's no reason to believe Brie Larson could, and banking on her ability to do it before the film is even finished is a gigantic gamble that has more than a whiff of feminist bullshit at Marvel.