New players have different calendars than us, to “test” different things.
Devs use to give new players some help, like more gold, better offers or outright better rewards. In your case they are testing different daily calendars, while other players have experienced different gear recipes (making it easier to upgrade heroes)
I personally find this unfair, since I wasn’t given any of these advantages when I started, but I guess it helps new players to push for higher levels on early game.
Answering your question, even if you don’t get our calendar for sometime, you can buy her frags sometimes on the alliance store. Since you only need 10 to unlock her, you could unlock her in the first week after joining an alliance, if lucky.