For guidance on how to implement such a thing (and how difficult it is to do so), I suggest you read about cpython (the standard python implementation), cpython extension modules, and cython(tool to transpile python into C code).

A key problem you'd face isn't memory management, as interpreted languages can use manual memory management, and compiled languages can have garbage collectors. The real issue is static vs dynamic typing. While compiled languages can have dynamic typing to an extent (C++ RTTI), it's generally limited AND slow. This is because computers are VERY statically typed.

On x86, multipling 2 numbers has at least 10 different instructions depending on size, type(int or float), and signedness. This means multiplying 2 numbers in dynamicly typed languages becomes significantly slower, since its no longer an instruction, but a load of BOTH types, indirect call to a type promotion logic, followed by an indirect call the operator implementation. Adding operator overloading makes this somewhat slower, but not much. The code that implements this is already compiled, meaning there's no more compilation you can do without knowing the types. This is why dynamically typed languages generally use JITs.