It is possible. IF get that IF you could ever get permission.
You ask Permission.
You pay the Fees
Main FEE would be Insurance. Expect that to be many many thousands.
You follow instructions.
Do not expect to be given hours at a time to use the tracks.
Would YOU be able to do it. Probably not.
It is technically possible. Work gangs go back and forth all the time.
They also do not normally make long distance pleasure rides .
You will have to be satisfied with out of service tracks or rarely used spur lines. They exist.
There are not many tracks to choose to get past the little obstacles called MOUNTAINS,
Abandoned? FIND the OWNER and ask. Tracks may have been removed or are not unusable.
Suggest you use a Bicycle.
Maybe try this over the Border. North of Orville.
Train crews did this for short journeys years ago. A few miles from the work camp to the work site. They now use trucks that switch to road at the next crossing.
Keep dreaming Doubtful you will ever be able to do a cross state journey. Maybe a few short ones.
It would be cheaper to rent a Private car and attach it to an Amtrak.Train Two routes out odf Spokane.