The most important demographic influence in the modern Portuguese seems to be the oldest one; current interpretation of Y-chromosome and mtDNA data suggests that the Portuguese have their origin in Paleolithic peoples that began arriving to the European continent around 45,000 years ago. All subsequent migrations did leave an impact, genetically and culturally, but the main population source of the Portuguese is still Paleolithic. Genetic studies show Portuguese populations not to be significantly different from other European populations.
When did people first start arriving in the European continent? (If the question is unanswerable, say "unanswerable")
45,000 years ago