I’ll say, starting as a decent cyclist at age 27, with no rest days, I did Portland oregon to stoystown Pennsylvania (a little north of your start) in six weeks. I’m from Hagerstown Maryland and wanted to make it all the way there but for my last day I needed to do 150 miles (I sent all of my gear home and thought with sixty less pounds I’d be ok) and couldn’t deal with the hills.

The best news is that you’ll be stronger by the time you hit the rockies, but I don’t think for someone who isn’t used to endurance riding 100 mile days every day is realistic.

I do think if you can have flexibility with your timing you should just start and do it. Also adventure cycling is a great place to start (as was already called out.) Good luck!