For certain meshes, this is (somewhat) possible without physics. For example, if you want to move a sphere around without interecting other objects, you can use some combination of constraints, GN, and perhaps other modifiers to shrinkwrap it outside a collection of those other "colliding" bodies, by a distance equal to the radius of the sphere. There are multiple techniques possible for this, but I won't go into great detail until understanding whether this would be an appropriate solution for your problem (need to know the shapes involved.)
This is only "somewhat" possible because base GN (and constraints) are not aware of what happened last frame, only this frame, and so even here, if you pull your sphere directly through a collider, it will teleport through rather than move around it. And, as mentioned, it depends heavily on the shape of the object or colliders-- it's not something I would dream of doing for an arbitrary shape.
With simulation nodes in GN, it is potentially possible to recreate collision physics, but doing so would be complicated and slow, and provide no benefit over physics-- you'd still need to bake the nodes or else scrub through the timeline in order.
The main reason for physics to exist is to solve collision problems. Physics are optimized for this, and so using physics is the best way to approach the problem.