First off you need to either have citizenship or permanent residency.
Then you can call this gun store, which is right around the corner from the license bureau.
Armas De Fuego
Av. Francia NO. 101
809-221-9042/227-9045
I don't know if they still do this, but a few years ago I took someone there in the AM, he bought a gun, and they sent someone with him to the license bureau. He had it in two weeks. But now it will take longer, as you need to go to a shooting range also. They make you take a urine test for drugs, and a psychiatric test
I have not been in this store in about three years, so call if you are interested. But this would cut through a lot of red tape, as he whisks you through it.