Unmarried in pa. father's name is not on the birth certificate (did not sign an Acknowlegment of Paternity, we are going for DNA test through domestic relations. Can the alleged father file for sole custody in the meantime?

He can file for it but it does not mean he can get sole custody.
He would have to prove mother unfit. Otherwise at best he will most likely get joint custody with a visitations schedule.

While awaiting the paternity results he can file for custody but under most state's laws, when a child's parents are not married, the mother has sole custody until the court orders otherwise.

Since there is no proof he is the father, he would not be awarded any rights till he is proven to be the father, He could file for it, pending the outcome of the DNA test