318 sb with a four barrel carb

I've had a similar issue with my car not starting during a certain window of time after shutting it off, usually around 30-45 minutes I think. I just put a brand new pump on it when I got the car, I usually just have to hold the gas down a bit and help it clear out. It's gotten a little better since I've been driving it. It used to be a total bear in a parking lot when it was tough starting. It would idle like crap and I'd have to keep my foot on it to keep it going, but as soon as you drove 30 mph for a block it would run like nothing ever happened.