The child support office can't find my baby's father to get this DNA test on the way, can I hire a lawyer that can help me get this on the way? I

If you hire an attorney, they will likely retain the services of a private investigator to assist in finding the Father and serving him with the necessary papers.  Once the Father is found, the Court could can compel him to submit to DNA testing.  However, the DNA testing may not be necessary.  Is he on the birth certificate and held himself out to be the father of the child for example.  Ulitmately the Department of Revenue may not have the resources to actively track down this individual.  A privately hired attorney could put specific effort towards this issue.