0x8027025a new console

Is it possible the problem is my internet connection, external hard drive, or even my xbox profile?

I would hope this isn’t the solution since i just traded up to this console because my previous one had the exact issue

Yes, i have done a hard reset of this console.

Is it possible the problem is my internet connection, external hard drive, or even my xbox profile?

I suspect your network hardware needs to be power cycled after you turn your console off and remove the power cable from the console.

Wait until your network is up and running before turning the console back on.

Also try a wired ethernet cable connection instead of WiFi.

Have you done a hard reset/power cycle on the console?

Press and hold the Xbox logo on the front of the console until it switches off, waiting atleast 30 seconds before switching it on again.

For more info on this error have a look in the link below.

https://support.xbox.com/en-CA/xbox-one/errors/error-code-8027025a

P.S. Congratulations on your new console.