I came across some writings of Philo, which I found very interesting, and wondered if there are any Jewish writings either around his time (circa 20 BCE to circa 50 CE) or before. I looked around and all I found were writings after Philo's time. My question is this: Are there any writings in Judaism say after Moses to the time of Philo? For those of you familiar with Christianity, it would be analogous of asking about the writings of the Church Fathers.
How about Ben Sira? It was composed around ~200 BCE, and is not considered part of the Jewish Bible.
Closer to Philo's time, the Mishna, compiled by R Yehuda HaNasi, is a collection of halakhic principles and sayings quoting Sages, including some living in the first two centuries CE, e.g., for the period which interests you
If you want to read a part of the Mishna more easily understandable without background, the Mishna tractate Ethics of the Fathers would be a very good place to start, (e.g., here or there). Its beginning actually lists the order of transmission of the Torah from Moses to later Sages, starting with Moshe, Joshua, the Elders, the Prophets, the Men of the Great Assembly and Shimon HaTzadik (ca. 300 BCE)