I have a 1990 SW20 N/A import.
 
And on a cold start in the morning it doesn't fire properly for about 5 seconds, its not spluttering, more like failing to raise RPM. It shudders and rumbles the car then its all good, its got new NGK plugs, just copper ones. new engine mount, had the head gasket replaced, and a carbon clean.....
 
it has been sitting for a bit, after the water pump blew and we replaced that. So i'm confused as to what it could be. 
Do i need to burn off any leftover gunk or something.
 
Need options????

  
      

Next time it does this try turning it off (as it is rumbling etc.), wait around 10 seconds and then try starting it again. If it then starts without a problem it is bound to be a cold start injector problem.  This used to happen with my SW20 occasionally but it didn't concern me as I just turned it off and tried again and it was fine.
 
If it is doing it every time though it's probably wise to get cold start injector checked out or replaced.

Possibly a worn out fuel pump

My car does this sometimes as well. 97 NA.
 
Cold start, it sounds like it's running on 3 cylinders. Really rough and low idle. If I apply some throttle to try and coax it into life, it doesn't like it and will misfire. If I leave it for a few minutes it will just start idling like normal. If I turn it off and restart straight away it always starts fine the 2nd time.
 
No idea what it is and it's been doing it on and off for at least a year or 2. No other issues so I've just left it alone.

My car has started doing the same thing, and I simply switch off and restart, as per Wiz's post.
That fixes it, so it looks like the CSI is faulty.
The climate has now turned cold, which is probably why it is now more noticeable.

My 97 NA use to do this. In my case I discovered it was the Caltex Vortex 98 fuel causing my cold start problems. So for an experiment, I filled up with BP Ultimate 98, no shuddering. The next tank I tried Shell V-power 98, no shuddering. I went back to Caltex Vortex 98 and the car shuddered on the first cold start every morning until the tank was empty. I could turn it off and restart the car with no problems on the second start. No idea why but using a different fuel has worked for me, possibly something you can try when you fill up next? 

Could you try unplugging the cold start injector wiring plug and see if it makes it worse or the same?
If the same then your problem is either the injector or a coolant sensor for the cold start (if there is one on the NA engine) 

Where abouts is the cold start injector

Mine does the same no matter on the fuel. Dosnt really do it in summer. 1990 jdm Na