#2 on b_Hill's post above, I can almost guarantee, is exactly what the issue is.
Today's fuel's are a lot more volatile than those from the late 70's, even today's REC-90 ethanol free gas is still formulated differently than the gas of that era. My '79 400 with its original carb does the same thing with cold starts and I have taken the carb off more times than I can count for various reasons and three times I've tested if the well plugs leaked (they've been marine-tex'd regardless, just in case) and they don't. That issue is not as common as everyone makes it out to be, especially on the later Quadrajet carburetors. It's probably not that, assuming you have the original carb.
One of the design flaws of the Quadrajet is that it has a very shallow fuel bowl, and the accelerator pump well is located rather high in proportion to the bottom of the fuel bowl. It doesn't take much evaporation of fuel (which is compounded by modern fuel volatility) after shut down to empty out just enough of the fuel bowl to compromise a good accelerator pump squirt. Fuel evaporation after shut down at operating temp is normal, and just so you know, this was even common back in the day. Lars Grimsrud is another authority on Quadrajet carbs after Cliff Ruggles, and he's mentioned quite a few times that even when these cars were new, they'd take 5-6 seconds of cranking to get them started if they sat on the dealership lots for 5+ days.
Most of these cars were daily driven when new, which didn't allow for enough time for a lot of fuel to evaporate for people to notice this issue. Doesn't help to live in a hot climate.
