As a Theravadan Buddhist I can say you are mistaken. There is the concept of rebirth in Buddhism and dependent origination which starts with actions that happened in the past. Including actions in past lives. In fact, there are multiple realms where one can be reborn like heaven, human, animal, hungry ghost, hell, etc.

https://en.wikipedia.org/wiki/Theravada#Core_teachings

https://en.wikipedia.org/wiki/Buddhist_cosmology