Is there a way to guess how the US Postal Service will route a package going cross-country?

I made an Ebay purchase yesterday from a guy who lives in Spokane, Washington. I live in the Southeastern US (near Atlanta, GA). He sent me the purchase using the US Post Office.

So how would the USPS route the box? My suspicion is that it would go from Spokane to Seattle, because that’s the next largest city with a big airport.

But after that, would it be put on a plane from Seattle to Atlanta? Would it go down to LAX and meet up with a lot other mail coming to the Atlanta area?

Of course, once it’s in Georgia they put it on a truck to my local post office and I’ll have it the next day.

Is there any way to divine how the USPS routes small packages?