According to Wikipedia,
Os Lusíadas is often regarded as Portugal's national epic, much as Virgil's Aeneid was for the Ancient Romans, or Homer's Iliad and Odyssey for the Ancient Greeks.
The article has a source for this information but says nothing about when people started to describe Os Lusíadas as Portugal's national epic. I checked the corresponding articles in the German Wikipedia, the Spanish Wikipedia, the French Wikipedia and the Dutch Wikipedia, none of which provide a source for such a claim (if they mention it at all).
The French Wikipedia article says,
À l’instar de l’Iliade ou de l’Odyssée pour la Grèce Antique ou l’Énéide pour Rome, Les Lusiades est une œuvre destinée à raconter et à glorifier la naissance et le destin de la nation et de l’Empire portugais.
In other words, the epic describes the birth and the destiny of the Portuguese nation and empire, which explains why it would come to be regarded as the national epic. But did the epic gain this status soon after its publication or only much later, e.g. after much of the empire had already been lost and people looked back on it with nostalgia?