Deterministic physics using built-in Unreal Engine physics isn’t particularly feasible, even for single-player games.
Networked Deterministic physics using built-in Unreal Engine is essentially impossible.
Your options when using Unreal Engine physics are either “crank up the replication rate and accept that you’ll be using a bit of bandwidth,” or “accept that physics entities will snap/correct/jump around.” (This is really the same for Chaos in 5.x and for PhysX in 4.x, not that different.)
Your option when you really do need deterministic physics, is to write your own physics engine. Because you want it to be deterministic, you’ll probably want to build it based on fixed-precision math – use an int64, treat the low 16 bits or so as fraction, for example. You will want to develop an actor component that syncs the actor setup (collision volumes, initial position) into your physics engine on startup, and then syncs the simulation results back out after each simulation step.
Because time steps in Unreal aren’t fixed, you’ll also need to translate between the fixed time steps you’ll need in your physics engine, and the current variable time in Unreal used for rendering, typically using either some interpolation with virtual time lag, or some extrapolation. You’ll probably also want to run your physics simulation at pretty high resolution to avoid too much discrepancy here; 240 Hz could be reasonable. (Typically this means you simulate more than one physics step in each render step)
For certain gameplay elements, you’re going to have to make up your mind – do you do triggers and interaction volumes using Unreal physics still (so they’ll be slightly out of sync with your main physics simulation) or do you want to mirror all the Unreal events (overlaps and so on) into and out of your simulation?
People are saying it’s “impossible,” but that’s not true. If you’re good at developing physics engines, you can totally do this, and the structure that Unreal already has in place for setting up objects in editors can be quite helpful as scaffolding, so you can focus on all the things that you need to do differently. If you were to write a physics engine from scratch (which people do do,) you’d have to develop a bunch of things on your own that you can just re-use from Unreal.
It is, of course, at least a year-long effort, and probably longer if you want advanced features, so make sure you know that this is how you want to spend your time. And if you haven’t really dived into a physics engine before, expect to spend another year ahead of this just to read the few books that exist, and learn how they work. Maybe pick apart a couple of open source ones (Bullet, ODE, etc) to get a feel for what the design and interface paradigms are.
As someone else said above: Good luck!