Are other birches there more advanced?

Yes, there are several other birches around the neighborhood, all covered in leaves. None are the same type of birch though, if that makes a difference.

I've seen that purple European birches are in leaf here in USDA 8, but they may still be expanding. Maybe in your zone the kind you have is not out yet. Otherwise, you might want to look for holes in the trunk, in case yours has borers.

Birches are just leafing out here, so if you're in eastern WA it's not too late yet. Nothing you can do to help it along, just be patient. Sometimes it takes a while for a new tree to synchronize with its new home. I once planted an apple tree that did not leaf out at all the next spring, not until fall! stupid tree. The year after that it was fine.

Scrape the bark of a twig with your thumbnail and see if it's green underneath. If not, try again farther down closer to the trunk, and keep going til you find green. Only if you don't find any green at all even on the trunk should you decide that the tree is dead. No reason to think it would be dead though, just maybe a little slow its first spring in its new home.