Sounds like she is settling in well, but leave her alone for about a day to settle in properly (no taming, just changing food and water). As cypher has said, she will be a Russian Hybrid but may resemble a Winter White or Campbells, however I'm not very good at identifying species so I am the wrong person to ask.
Everyone has given you good advice so far, but there are a couple of things I would add.
1) The fact she is sitting/sleeping out in the open is a good thing. It shows she is already comfortable in her new surroundings with you around. Larry-Jasper has been known to fall asleep in his sand bath and really enjoys his.
2) While she is still settling in, avoid waking her as it will seem like you are a predator. I wrote a really long taming advice post yesterday, if you want me to post that here or DM you it, let me know. Don't worry about her just making a burrow in bedding, it just shows she enjoys digging, but it will be difficult to wake her without destroying her nest, which will scare her or annoy her (she might bite). She may move her nest around a few times while she is still exploring her cage, but again, this is normal.
3) If you have just brought her home and have woken her a few times, it is likely she will be irritable and tired. It is very stressful and exhausting for a hamster to be brought home so that is why she won't be too active for the next few days. Just leave her alone for the minute to settle in. I know how tempting it is to want to play with them. I don't think starting taming this early on is a good idea, unless you are just giving treats when she is awake.
If you do need to wake her up, there is a kinder way of doing it. I take a sunflower or pumpkin seed and either drop it on something hard in the cage (wheel, wooden toy) near his nest, or gently put it near the entrance of his nest. The noise of his favourite treat will wake him, but he doesn't mind because he gets his favourite treat. This normally gets him awake and out to see me, but only because he has settled in and is very tame.
EDIT: Forgot to add, Milly is super cute
and congratulations on bringing her home
!