My new cherry tree just arrived and all of its new growth seems to be in bunches of super close and curly leaves. Is this normal? There are flowers budding at the top which makes me think the tree isn’t dying but I’m new to this and wanted to see if anyone could offer insight.
No it's not normal at all. There are various causes for cherry leaves curling - the two most common are cherry aphid infestation, and cherry leaf curl fungal disease. It may be that your tree had an infestation of cherry aphid before it was supplied to you, but I'm not seeing aphids at the moment. I particularly don't like the crinkled effect on the leaves, which might suggest a viral infection (sweet cherry crinkle disease) - frankly, I'd return it and ask for a healthier one.
Causes for cherry leaves curling listed here https://homeguides.sfgate.com/leaf-curl-disease-cherry-trees-55808.html