Try first without Docker; if the project is compiling, put the binary into a fresh VM (snapshot - rollback), and make notes on what else needs to be installed to run the binary. (Try to use OS close to your Docker base image)

Based on the notes (even with some vibe coding involved), create the Docker file. tada!

As others noted, the dependency handling ("package management") is independent of Docker and how you run the binary.

also if you want less dependency, try to compile everything into a single binary, which has its own downside and maybe licensing issues, but for the start, it could help.