Owner training is an option but very difficult without paying for expensive trainers to assist. There are organisations that provide them and help you fund raise

You probably won't be able to owner train the dog on your own unless you have lots of experience with training dogs. You'd need more training experience than the average dog owner to do it alone. The only other cheaper option is to get a dog through an organization that'll help you with the cost, but I'm not sure if they'd let you get a dog being homeless. I would suggest waiting to get a service dog until you're in a better place to be able to care for the dog. A service dog isn't the same as something like a wheelchair. They're a living animal that need yearly vet appointments, vet appointments if they get sick, food, vaccines, flea and tick treatment, heartworm prevention, and more. That's a lot of money and time. Before deciding to get a service dog you really need to think about if you're able to pay for the cost of a dog and if you have the time to actually take care of the dog.