On screen: Sorry, we can't sign you in right now. Try again later. (0x87DD0006)
When you see this one, the problem is most often on the operator's side and there is nothing on your machine to fix. Check the live status first.
Xbox network authentication failed. Your console holds a valid Microsoft account token but could not exchange it for an Xbox service token.
Microsoft's own first instruction for this code is to check the Xbox status, which tells you where they expect the fault to be.
If the status page shows limitations on sign-in or account services, wait — nothing local will help. If status is green and only one profile is affected, remove and re-add that profile. If you hit it during a system update or first-time setup, it is the update path rather than the network.
Operator documentation: support.xbox.com. Microsoft's page says: “This may mean that there was a service outage just before you tried to sign in.” Note the URL has no 0x prefix — support.xbox.com/en-US/help/errors/error-code-0x87dd0006 is a 404, while the equivalent page for 0x87e5002b does carry the prefix. Their scheme is inconsistent, so guessing these URLs does not work.
Xbox network authentication failed. Your console holds a valid Microsoft account token but could not exchange it for an Xbox service token.
When you see this one, the problem is most often on the operator's side and there is nothing on your machine to fix. Check the live status first.
Start with: Check Xbox status for sign-in and account services. Microsoft puts this first for a reason.