There's lots, but it depends on what you consider to be evidence.

If you're talking about physical evidence, ancient battlefields are notoriously hard to locate. The locations in the literary sources are mainly just given as references to nearby settlements. Zama was just the closest settlement to the battle named after it, and so there's a large area that it could be located in. Even if somebody started digging in the right place, most of the remnants of even large battles can be hard to find. Iron rusts, leather rots, and most equipment is taken from the field anyway. Bodies are often moved, disposed of, left to rot or scattered by time. Even in Europe, to my knowledge no mass graves have been found after any of the countless major battles that were fought there in antiquity. We shouldn't be surprised we haven't found Zama: we haven't even found Cannae, and that's possibly one of the most studied and searched for battles in ancient European history.

However, there are a great deal of literary sources, but the only one you should need to convince you is Polybius. Polybius lived in Rome for a long time after he was taken from Greece as a hostage. Polybius' Roman host was Lucius Aemelius Paulus Macedonicus, son of the consul who died at Cannae. Macedonicus' biological son was Scipio Aemelianus, who had also been adopted by Publius Cornelius Scipio, the son of Scipio Africanus who defeated Hannibal at Zama (confused yet? I know I am...) Polybius formed a close bond with Scipio Aemelianus, and brought him as a special advisor when the latter destroyed Carthage in 146 BC. As a trusted friend of the family of the man who beat Hannibal at Zama and an expert in Roman warfare, Polybius was therefore as uniquely positioned to comment on the details of Zama as anyone possibly could be without having been there. Polybius also has a good reputation for accuracy. So if Polybius says it happened in such detail, it's pretty safe to assume it happened.