2.2 sonoma wont start when it cold

aLL FUSES GOOD.
all cold engines race high ,engine cold and the more cold the more high RPM. 1500 is PAR for RPM cold, is yours higher?
black SOOT is a huge bad RICH sign. of greatly needed engine service.
no code told P03xx what is XX.? (sad face)
we can';t guess codes we need to see them. sorry and all off them.
I thank also your scan tool is not certified for GM OEM scan codes.
P1xx up.p2XX ?
or is super old scanner useless
or just cheap $17 code reader ? also useless in the real world.

also did you know P0300 to P0306 means misfire. (weak combustion) lots of clauses.
ever do full tune up, in 20 years, spark plugs , spark wires
distrib. cap and rotor? ICM bad,?
?????
Map sensor clogged
IAC valve stuck open , RPM not regulated.

Fuel pressure was low, how low?, not told PSI
low does not cause rich burn but sure lean burn and misfire sure.
spec is.fuel real PSI test is 60-66?psi. RUNNING engine.
if not pump or FPR are bad. yes pumps can fail weak easy.
the test is called the Injector fuel pressure balance test in the SM, service manual.
the rules are.(gas)_
1: good engine, (compression at spec) EGR not stuck open and CATS not melted closed.
2: spark good, we can not burn fuel with dead or weak spark.
we call this a tune up,. (or doing the service points (today)
3: bad fueling, last fuel is last. in the due to Physics.
bad fueling can be caused by (short list)
bad MAF , or MAP, FPR, PUMP, or injectors leaking or clogged.
IAC stuck makes idle controls dead.
to find it take real tools , and gauges, a real scan tool , 2008 or newer OBD2 scan tool is best, for sure GM rated
GM has its own OEM factory codes. (vast)
or get the car serviced in a shop.,,, Bingo they have the tools!

here is your spark schematic
all these can produce P03xx codes too, but was never told.

https://imgur.com/a/gw0cHYR

2001-2004 gmc sonoma 4.3 [X, W Eng.] fuel system specs: 60-66 psi when you turn the ignition key (fuel pump) on without starting the engine. If fuel pressure drops back down quickly after fuel pump stops working (works for only 5 sec.) then you have a bad fuel pump or leaking injector spider.

Check the fuel fliter

This sounds like a signal for the cold start routine is not reaching the brain. Your SUV uses water temperature to tell the brain the engine is cold. There are 2 sensors for the water, one for the gauge and one for the computer.

The signal makes the fuel mix rich and speeds up the idle. It works like a choke. Go to Autozone or Oreillys and get a free scan. You should ask about a starter draw test too. When they scan your SUV they can show you where the sensor you need is located. Just change it and the next cold start will be either good or still bad.

If the start is still bad you have to look for other reasons. The fuel pressure is one thing to measure and this will require a pressure gauge. Check the Intake manifold for vacuum leaks after the engine is running with a water spray bottle on the seams of the part. A leak will affect the RPM. The colder weather can cause a marginal leak into a bigger problem making leak. Then when the engine does run, the heat expands all the parts and the motor runs great. But cold it does not draw the fuel in properly and starts poorly.

Hopefully your problem will be solved with my first solution. Would be interested in what you found.

problems with the choke, to low fuel float level in carburator, timing to retarded or just problems with your battery or starter if it doesnt crank fast enough

Yes fuel pump is going bad
Darn electrical parts there good one day and than there bad another
3 things an engine needs to run
AIR FUEL SPARK

DO A FUEL PRESSURE CHECK ANYWAY, ALSO THE RELAY MAY BE GETTING HOT CHECK CODES TOO.

check the play in the distributor,and check that the fuel pressure is normal

check fuel pressure on fuel rail to ensure good fuel pressure according to specs for van. also check fuel pressure regulator look for fuel coming out of the vaccum line. if it is then replace it

The iat (intake air temperature) is located on the air filter housing. If its reading high its probably unplugged