States only pay if you're on unemployment and meet the requirements they stipulate. It's not cheap either. CDL schools cost about 7k now, with no guarantees of passing and no guarantee of a job if you do pass.
I'd recommend the opposite and let a company pay for it. A year isn't that long and if you decide to not stay, you pay for it. You'd be paying it you went and did it on your own so no harm no foul.
There's also no guarantee that a company like saia would take somebody with a CDL and no experience. I went to FedEx to get my CDL and I have no regrets. Guaranteed a good job with them upon completion and they paid me to train and get my license. That year went by quick.