Some would say the past story is untrue because it comes from Izzi's book.
However, while there is this to consider, most of the evidence appears in favor of supporting the past story as being true.
1) One big piece of evidence to support the past story being true is that the compound with the extract from the Guatemalan tree actually does work on the monkey in the present story. This compound reverses aging and even cures cancer. Thus it validates the existence of the Tree of Life in the past story from Izzi's book.
2) There really were Conquistadors, Inquisitors, Mayans, political battles for control in Spain, and Spanish territories in the Americas. Darren Aronofksy used the book the "True History of the Conquest of New Spain" by Bernal Diaz del Castillo which is a real account of a conquistador's journey as research for writing his past story. This supports Izzi's book being true.
3) In the film Dr. Thomas of the present story is shown to be affected deeply by Izzi's book, almost as if it were a real story of the distant past. In one sequence at the beginning of the film Dr. Thomas looks at the light from a bulb and appears to have a momentary hallucination seeing the Xibalba nebula up close in great detail. His face contorts into shock as he comes to a realization. Thomas seeing the Xibalba nebula in a hallucination so early in the film is important because this occurs before Izzi shows Thomas through a telescope Xibalba. In another sequence shortly after reading a few chapters of Izzis book,Thomas has a vivid dream that startles him causing him to awaken petrified. Thus, it appears as if Thomas is recalling the past life vision of Tomas. Even with the parallels between the book and his life, it defies convention that Thomas who is a man of science that doesnt believe in Izzi's stories would be terrified by a fictional story of the past to the point that it causes him to have hallucinations, especially since this starts occurring before Thomas has even started reading the book unless Thomas has actually, somehow, experienced such a story of the past.
4) In "The Fountain" graphic novel, which Director Darren Aronofsky has called the director's cut of his film, Tom of the future story is shown to have a massive scar on his chest that came from Tomas of the past story getting sliced by the fire sword of the Mayan high priest. Thus in the graphic novel if the future story is accepted as real, then the past story must be real as well, otherwise Tom wouldn't have Tomas identical scar.
5) If the future story in the film is to be accepted as real then the past story must be real as well as the future validates the past. Everything in the Mayan myth of creation Izzi told Dr. Thomas in the present story at the museum that makes up the basis of her book is presented in the future. The future story shows Tom as a godlike figure with a Tree of Life that makes Tom immortal so long as he eats from it. This is identical to the power of the Tree of Life mentioned in Izzi's book. Tom just like in the myth from the book is shown to be the First Father that must sacrifice himself so that the Tree of Life may live. There are other details as well that point to this conclusion. Tom uses a quill ro mark the ring tattoos on his body which references Tomas in the past story using a quill to write a letter. Tom is also careful with how much sap he takes from the Tree of Life, which references the event of the past story whem Tomas dranked so much sap from the Tree of Life that he was buried by flowers. Additionally, Tom recalls the past story in vivid detail and accepts it as real as the present story.
6) The past story appears to be treated as equal to the present and future story therefore it must be real. The past story is shown in the film to be on equal footing with the other stories. In particular there is a scene in the past of Tomas racing on horseback towards a castle that is filmed in a very specific manner. This specific manner of filming is repeated again in the present story when Tomas races by car to the hospital and again in the future story when Tom races in the tree ship sphere towards Xibalba. While some would argue this is merely film technique with no meaning, Aronofsky has commented that he made conscious decisions that elicit meaning when filming. Thus, if the past story was not real, it stands to reason that Aronofsky would have filmed the past sequence differently to illustrate that it isn't real and not in the same style as he did with the other scenes in the other stories. For example one way fictional stories have been showcased to not be real in movies is by having the fictional story be depicted in the colors of black and white, while the rest of the film is in color.
7) According to Aronofsky understanding the film is in the details, the details of Izzi's book appear to provide evidence that the past story is true. In real life there have been some people that at some point in their life have started recalling memories of an apparent past life in another age in another body. Some of these people come to believe in reincarnation. One of the methods a person faced with the probability of being reincarnated comes to understand their past life is by writing their resurging past life memories in a diary. Writing your experiences in a diary is a way of recording your experiences so that they may not be stated as real and forgotten. All this is important because Izzi's book doesnt come in the binding of traditional fiction. She didnt write her story on a computer and then simply put it into a standard non-lined printed paperback novel with an introduction. Instead, Izzi's book was written by hand in a hardcover diary on lined paper with ink from a pen that carries a Mayan symbol for a tip. The difference is significant because if Aronofsky who is a master of details wanted us to believe the past story was fiction undoubtedly he would have had Izzi write her book on a computer or laptop. Instead Aronofsky binds the past story as if it was real in a diary. Further not once in the film is Izzi's book called a novel. This is important because writers use the term novel to refer specifically to a fictional work and the term book to refer specifically to a nonfiction work. Two examples are Stephen King's novel "The Stand" or Carl Bernstein's book "All the President's Men". If Izzi's work was fictional she would have called it a novel, just as writers generally have done for centuries.