Like other historians writing about the age of encounter and conquest that swept across the Americas from the late 15th century, Caroline Dodds Pennock begins her new book with an account of a voyage across the Atlantic Ocean. What is different is that this journey, of 1519, was from west to east – from the so-called “New World” back towards Europe.

The ship was loaded with so much treasure that gold was used as ballast; a first addictive hit of the vast mineral wealth of the Americas that was to flow around an increasingly interconnected global economy. However, it is the people on board, rather than the treasure in the hold, that are the focus here: not the European conquistadors but the indigenous people, in this case a group of Totonac men and women from what is now Mexico.

The Totonacs, who were later presented to the court of Charles V, the Holy Roman Emperor, were not the first indigenous Americans to arrive in Europe. In his early transatlantic voyages in the 1490s Christopher Columbus abducted dozens of Taíno people from what today are the Bahamas and Cuba. Over the course of his long and disturbing career he was to enslave thousands more.

On Savage Shores is a work of historical recovery. It paints these marginalised figures back on to history’s canvas, complicating familiar narratives of “exploration” and “discovery”. It introduces us to the Brazilians who met Henry VIII and the Inuit man who was brought to late 16th-century Bristol and hunted ducks on the River Avon. We learn of the thousands of others who arrived as intermediaries and translators, diplomats and servants.

Pennock uncovers their journeys and where possible their motivations, arguing forcefully that they should not only be written back into history but in some cases regarded as explorers in their own right; people who travelled to what were, after all, distant and unfamiliar lands, where they sought to understand new languages and make sense of foreign customs.

She also reveals that some of them never left. Their remains lie in cemeteries across Europe. In the churchyard of St Olave’s in the City of London, for example, not far from where Samuel Pepys was later to be laid to rest, are the graves of two Inuit people who died in London in the 1570s, having been abducted from their homeland in what is today Canada.

The history examined here has been carefully assembled from shattered fragments; tiny shards of historical detail from which Pennock builds a larger mosaic. The few biographies that emerge vividly from the available sources tend to do so only momentarily, before their subjects slip back into the darkness of unknowability – their fates and the final acts of their lives unrecorded.

Yet despite this, Pennock deftly picks out men and women who in traditional accounts are mentioned only in passing. Figures such as Diego Colón, a Taíno man from an elite family who was abducted by Columbus, and who became an interpreter and part of the Columbus household. And Malintzin, a woman of the Nahua people, whose skills as a translator allowed the conquistador Hernán Cortés to communicate with both his allies and enemies during the conquest of the Aztec empire.

On Savage Shores repeatedly implores the reader to attempt to engage with a simple but fundamental question – what must these encounters and experiences have been like for them? Especially for those who arrived in Europe as their own societies were being decimated by disease and conquest? What did they make of Europe, the grandeur of royal courts and the poverty of the teeming cites?

In one of her early chapters Pennock urges us to to “imagine the sixteenth century a little differently”. Despite the enormous challenges presented by the sources and the inevitably fragmentary nature of the lives that appear from within them, few books make as compelling a case for such a reimagining.

• On Savage Shores: How Indigenous Americans Discovered Europe by Caroline Dodds Pennock is published by Orion (£22). To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.