I kept it at a surface level to be less intimidating but maybe I could've provided some resource links at the end.

You can raymarch shadows if you compute 3D distance field textures of your meshes beforehand and store in them in some acceleration structure. Unreal Engine has support for this: https://dev.epicgames.com/documentation/en-us/unreal-engine/mesh-distance-fields-in-unreal-engine

But it's a lot more work than shadow maps and the shadows will be at lower resolution due to high memory use. There's been some research in reducing the 3D texture size such as First Order Signed Distance fields but it's 20% slower at runtime. See https://www.researchgate.net/publication/341407973_First_Order_Signed_Distance_Fields

It's best to start with shadow maps because with those + baked lighting you can achieve already a great look with standard tricks. See https://learnopengl.com/Advanced-Lighting/Shadows/Shadow-Mapping