I think it was a good decision to claim the 10 points (disabled vet at 30% or greater). Essentially it places you higher in the line of selection and you are correct most people can't even qualify for fed jobs as they don't accept applications from anyone. There are a couple different Veterans Preference hiring authorities, you may want to research. Some authorities allow hiring a vet without competition, of course the Agency has to choose to advertise the position this way, but some will.
https://www.opm.gov/policy-data-oversight/hiring-authorities/veterans-authorities/