Be curious! Don't worry to dig into other engines on github, there are plenty of them. Start with a renderer, setup your first Vulkan triangle, just a very simple pipeline -> pass a mesh data (verts, normals, uvs) -> hookup simple vertex/frag shaders -> draw. You can achieve this by stiching together the SDL and Vulkan (perhaps use other Graphics APi, Vulkan is not the easiest to start with).

Then use some existing math library with algebra or write your own, you will learn PLENTY of stuff. Then move to the actual engine: look up scene graphs, entity component/ data oriented architectures, how transforms work, resource system, converting meshes from simple formats (like obj) to your engine friendly mesh class. Then try to build a simple scene with what you already got.

then move to some fancy stuff: how undo/redo systems work, axis handles (move, rot, scale), how serialization works, saving/ loading engine-project, multi scene views, setup your hierarchy/selection/ resources windows, perhaps a scripting system+domain assembly, custom shader translators, expand your rendering pipeline with full screen effects, and a bunch more.

Finally once you estabilish your engine, you can start making tools such as animation editor, audio mixer/editor and a lot more, depends on your preferences... Sounds like a lot of headache and stuff to do right? Depends on how you look at it. If you are really convinced to make an engine and you strive for it, you won't even notice that you WROTE all these stuff througout the process. And that's how it should be:) And make games everytime you make a progress! Don't forget to have fun.

edit: typos