It's not the 02 sensor-- the signal from the O2 sensor isn't useful until the sensor reaches a particular temperature range, so it isn't used in the fuel/air mixture enrichment feedback loop until the engine is warmed up.

The biggest risk with a malfunctioning O2 sensor is that the car will run rich and ruin your catalytic converter. I've done 02 sensors in the driveway in winter here on the other side of Lake Ontario. Just give the sensor a small shot of good penetrating oil (P'Blaster or Kroil, not WD-40) for a few days before you do the job.

Good luck!

Possibly lawn mower syndrome.

You start a 5 cylinder white engine and only run it for a short time,

Like if you move the car to get your lawn mower out of the garage.

Back in the 850 days, this was a frequent post.

It happened to me, I moved my car to the shade when I was waxing it. I had it towed to a dealer - they got it started, warmed up and then changed the oil and put in new plugs. (Plug fouling and oil dilution)

After that, a family rule was never start an 850 unless you are going to warm it up fully.

The car may actually crank faster than normal because some of the valves are stuck open.

My theory - When an aluminum engine runs for a very short time, the only things that get hot are the exhaust valves - they stick in the valve guides.

Holding the pedal to the floor during starting shuts off fuel flow, and the engine clears itself.

Crank a little longer than normal, pause, crank a little more than normal, pause ... repeat - Keep the gas pedal on the floor.

Twenty seconds sounds like the right time. Get your repairs done before you go chasing windmills.

The O2 sensor tells the computer how rich/lean the mixture is supposed to be. At cold start, extra fuel is introduced which may cause fouled plugs to become wet and not fire.

Replace the O2 sensor as soon as possible. You want to wear gloves anyway...

If the heater core is not leaking very much, wait until the end of this month but before your trip. Give yourself 2 hours for the job.

Check your vacuum lines, all of them. If you have a turbo, verify that the 3 lines to the turbo are not cracked. A crack in any line will also cause the engine to run rich.
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Keeping it running is better than buying new