Good chance replacing the fuel pump will fix this. A shop would first make a fuel pressure hold test. If the fuel pressure isn’t holding to spec after turning the engine off, they’d do add’l tests to determine if it was the pump or a leaking injector etc. But if you don’t want to do all that and just want the problem fixed, if you are lucky a replacement fuel pump may well do the trick. As mentioned above, the O2 sensor signals are normal. The first one is before the cat and registers every too-lean/too-rich transition as the computer tries to maintain the correct air/fuel ratio; the second one is the post-cat sensor, which doesn’t register the immediate too-rich, too-lean conditions the first one sees. The engine has to run well even with the O2 sensors not working b/c they don’t work until they heat up, so the first 5 minutes or so after starting the car the O2 sensors aren’t used. If you want an assessment of the fuel mixture function, that’s called a fuel-trim measurement. Any good shop can do that for you.