Got an 89 Corolla that just had its carburetor rebuilt professionally, but has trouble starting first thing. I can't remember if this was a problem prior to the carb rebuild. It's a friend's car and she's away. Want to get it running well before she returns.
When first cranked in the morning, it won't start, but if I stop cranking and then crank again, it will start. In other words, it's on the second crank that it starts. After that, it will start well on subsequent starts.
I'm thinking it may be a fuel pump problem? And after the first crank, it builds up enough pressure to start? But then why wouldn't it start at the end of the first crank, but then start on the second crank?

Any suggestions on solving this puzzle would be greatly appreciated.

. Replace the fuel filter.

. Start the car this way: 1) Turn the ignition switch to ON, until the fuel pump stops running; then, 2) turn the ignition switch to START. This builds-up the fuel pressure first.

Thanks for the reply. It's a mechanical pump. I have replaced the filter.

That car has a cold start injector.
If the car has been sitting for too long that extra injector may have become stuck seated. Diagnosing that requires more experience than the average DIYer so you may need to seek professional help.
Make certain that the coolant is the correct mixture and filled without any air trapped.