I believe I read this in the early 2000s in either Kentucky or Ohio as a paperback book, published in English. I want to say that the book was green primarily in color. As I recall it, the book opens with a prologue showing the father travelling to a hidden city in the jungle (I can't remember if it was Africa or South America. I have Mayincatec overtones in my head, but I remember the description of the jungle being more Darkest Africa) which he had discovered with a great treasure, and then something happens and he dies. This leads to a letter being sent to his children (of which there were at least two adult sons, but I think there was a daughter as well) giving them clues to the location of the city and the treasures within.
One of the sons was our protagonist, who seemed like a fairly decent guy. I think he might have been a journalist? He partly embarks on the quest because he wants to know who his father really was. One of the other sons ran either a church or a charismatic cult, and dies shortly into entering the jungle while navigating a river (I remember it as him being cynical about his actual religion, but having sort of bought into his own myth of being destined for greatness, and his hubris leads to him not showing up with adequate supplies). Chiefly, I remember the protagonist being positioned as the only decent one of the lot.
The city itself is located across a canyon, or within a pit, with a bridge leading into it. I mainly remember that because at the climax of the book, said bridge starts to disintegrate, I think because they triggered a doomsday trap, ultimately destroying the city. The other thing that I remember about the city was that, in a rather predictable twist, the father is not actually dead, and was treating this as a test. I remember him not being very concerned that some of his children had died in pursuit of this quest.
The sci-fi/fantasy aspect was that the city was also supposed to have ancient lost technology that bordered on magic, although I don't remember the details.
