If Nathan Drake's younger age in the Uncharted film weren't enough to establish its status as a prequel, the way he's introduced to important characters and elements from the games clinches it. A key detail in the movie is Nate's aversion to killing — something never referenced in the games — which he seems to get over well enough by the end when he finally uses a gun to defend himself. This is a younger, less experienced Nathan Drake; he's just coming into his own before becoming the man introduced to audiences in the Uncharted games.
Tom Holland's casting as Nathan Drake in Uncharted fits right in with what the movie establishes of the character's age. The Uncharted movie shies away from too many specifics about Nathan Drake's age, but it says that he and Sam separate when Nathan is 10 years old. The action then takes up 15 years later, suggesting an age of around 25 years old for Nate. While Holland has frequently portrayed younger characters, he's in his mid-twenties and fits the bill nicely for what Uncharted tries to establish in the Nathan Drake origin story established in the movie.
It has been confirmed a number of times that Nathan Drake's age is 31 in the first Uncharted video game. While the continuity between the two is fairly loose, the adaptation still shows a younger, greener Nathan Drake in the Uncharted movie than the one established in the game franchise. A potential Uncharted 2 movie would likely show him growing further into the character audiences first met in the games.
Set somewhere between five and six years before the events of the first video game, the Uncharted movie makes credible sense as an introduction of Nathan Drake's character: he's still becoming the action hero that audiences recognize and love. Tom Holland does admirably in this sense. Nate isn't yet who he will become, but by the end of the first Uncharted movie, he's closer to becoming a familiar version of Nathan Drake.