The strange ingredients are garum [2] and asafoetida [3]. The former is just a fish sauce, so that's not hard to substitute, but you have to find asafoetida on the Internet or at an Indian food store.
1. https://www.youtube.com/watch?v=6LynenQ5h2Y
the parthian chicken was stupid easy and tasty
I've also made the Babylonian stew from this recipe, and it's rich and hearty. It's easy to see how this would knock the...sandals off of ancient people.
Other ancient recipes...let's just say that humans have very much not held the same tastes over the eons. Some recipes were incongruent or sweet and savory in a strange way, or simply a flex about how many spices you had access to and cold throw in a dish, not about what it really tasted like. YMMV.