Pretty well covered already, I'll add though.
I'm curious what exactly was the nature of the injury how much tendon vs muscle vs bone was involved and what did they do in the surgery? Regardless of that my thoughts below all apply, it's assumed you will get some specific rehab guidance once the cast comes off.
For at least another week focus on keeping it super stable, there are reasons they put you in a cast, which I'm sure you understand. Somewhat like compounded interest your early contributions have the biggest effect on those reasons. The sacrifice of relative inactivity early on will pay off in the long run more than getting a bit soft right now will hurt you. Think of the initial healing as the base for all the forces going through there for years to come.
And don't try to outsmart the healing by figuring out some way to do back chest or shoulder exercises with the cast on for now, your bicep lengthens and shortens through those ranges whether you want it to or not, passive motion still generates small forces.
That philosophy goes for all recovery components, sleep, hydration, nutrition, PED's etc. Get all that shit perfect right now, no couple of beers with the boys or staying up all night watching movies. You don't strike me as that kind of guy but boredom can lead to poor choices.
One thing to do that may seem like an exception to the stability thing is to wiggle your finger's a lot, Keep your arm stable but open and close your hands, do dexterity movements with your fingers but no load (for some weeks). There are tons of finger patterns that a physio would put you thru, make up your own or look them up. No load means no squeezing a ball or opening hands against rubber bands etc. (yet) The purpose of this is to keep the nerve pathways firing through your arm.
Unfortunately you won't be firing much for the biceps or triceps for a while but at least its something.
After that you can add something that will work the pathways to your bi's but it's very hard to do if you can't already do it, there is an element of risk if you screw up. Extremely hard to do with the triceps in that position.
It's a VERY light flexing of the bicep, a mere flick washout moving your arm or putting any puling force into it. You know how guys flick there pecs while still keeping them loose? Same thing. Might not even be worth trying if you couldn't do it before, or maybe do it with the other arm to learn how to do it safely first. NO STRAIN!
Apologies for the wall of text but the early stages are so important, tiny little things matter and add up. I've been through this stuff many times both personally and with others.
All the best to you.
