If you are lucky enough that the large and complex codebase has extensive system-level and unit-tests, then that is where I would start.
Hopefully it is easy to get the codebase up and running so that you can explore it hands-on and try both happy-path cases and what happens when things go awry.
Walk through a feature of the code manually or step through it using a debugger while drawing boxes on how stuff fits together, and what the main building blocks are.
It will always take time to really understand a new large and complex codebase. If it is high-quality code it is easier, if you have experience with similar products it is easier. But to really feel that I grasp the really good parts and the dark and dangerous corners of a new codebase always takes me months.
Hopefully it is easy to get the codebase up and running so that you can explore it hands-on and try both happy-path cases and what happens when things go awry.
Walk through a feature of the code manually or step through it using a debugger while drawing boxes on how stuff fits together, and what the main building blocks are.
It will always take time to really understand a new large and complex codebase. If it is high-quality code it is easier, if you have experience with similar products it is easier. But to really feel that I grasp the really good parts and the dark and dangerous corners of a new codebase always takes me months.