O2 sensors don't do anything until it's fully warmed up, when you are experiencing the trouble it's before the O2 sensors are doing anything. Not an O2 trouble.
Put a fuel pressure gauge on the rail. Run it for a moment, shut it off. I'll bet the pressure drops down to nothing in a moment or so.
I suspect a fuel injector is leaking, gas is puddling on the piston top, when you crank it, it splashes onto the plug, fouling it. Running a moment eventually clears the fouling.
After a longer sitting that fuel drains down into the crankcase (smell the oil) and doesn't foul the plug when you start it - no more puddle.
Before panicking, try running a strong dose of Techron in the gas tank (parts house - better stuff than all the others combined,) - it may dissolve what's holding the injector open. Pouring it down the throat will not do the trick, it has to go through the fuel system. Normally I'm against adding cleaners since the fuel has enough in it already (unless it's old and stale,) but in this case you need extra cleaning. Cleaner may not work if it's something that won't dissolve, dirt, metal fragment, sand etc. But it's worth a try.
To find out WHICH injector is leaking, run it, shut it off, start it so it misfires, shut it off while it's still misfiring, then quick - remove each plug looking for one being too wet.
You may have to remove the injector to clean it - or replace it. (Do not poke things in the injector's hole!)
After you solve it, change the oil.