Cardial ware people crossed the Gibraltar Strait and went up the coast of southern Protugal
but very little is known about Neolithic Galicia

my guess : herders from southern France or from the Ebro arrived there

In the Cantabrian region, which includes the northern coast, Neolithization is dated to 8,000-4,000 BP, and there it is the result of a complex mosaic process in which hunters and gatherers lived along with settlers [25]. The first domestic animals of this region date to around 7,000 BP and were mostly ovicaprines, which were later followed by ***s and cattle [1]. However, much less is known about the region adjacent to Cantabria, Galicia, because no Neolithic sites have been identified in this region yet [26]. The oldest genetic information for Galicia is from the Chalcolithic period. It dates to 5,950-5,050 years BP and therefore to a time period in which settlers with domestic livestock were much more common than other forms of human societies [26].