I liked Superman, but the setup for Supergirl was awful (will still watch I though)!.You are correct. Krypton had a red son so they had no powers there either.
She had to get shuttles or space ships, usually hitching a ride with someone. It'll be shown and explained in her movie properly.
Comic fans of Supergirl will be much less, I suspect, than Superman. Most people will know the Helen Slater film only. It was an OK film, for the time. Leaning into the comics for her film is not a good idea imo.
If it's set on Earth then I'll be wrong, but I suspect it's all gonna be in some other planet/universe.
rp2009