My new rescue dog won't pee or poop after adoption. Is this normal?

I would not be overly concerned about this just yet. Dogs can hold it for a pretty long period of time. It is not great for them to do so but it should not be harmful at this stage. Are you sure she hasn't gone somewhere in the house?

If you are taking her out on a leash, she may not be used to going on a leash - this happens a lot. So you may have to have her off leash. Don't make too much of a big deal when you take her out. Only say whatever word you want to cue her to use the bathroom like "go potty". Do not say or do anything else. Once she goes give her a good treat of something she likes.

If you don't have an off leash area then I suggest you do the same as above just on leash instead of off. Try to take her to a spot where other dogs have gone as this usually stimulates them to go.

Urination is most important. If she goes 24 hours without urinating you need to get her to a vet. It may be days before she defecates and that is not as concerning.

Hope this helps. Best wishes.