Fuel pump parked up hill
Unless it has been sitting for an extended period of time, the carb bowls should be full of fueland it wouldn't even need a fuel pump to start . It should be able to run a minute or two just with the fuel in the carb.
There's a nice thought that we all wish was true everywhere. :-)
Unfortunatly living in AZ changes that. (Especially in the valley)
Ed, one of the best things I ever did for my first starts is an electric pump.
It is just an average generic pump that I mounted on the side of one of my subframe connectors right under the passenger floor area (my fuel line was exposed right there)
I turn on the ignition and wait a second or two till the pump sound changes, once or twice to the floor with the pedal depending on how cold it is and hit the key.
Fires right up every time.
Just in case you happen run out of gas, the electric pump will get fuel back to the carb a lot faster, and you don't have to even crank the engine.
The only other way to solve that is with an anti drainback valve, but you will still be low in the float bowls till the pump fills it. (Still a delay) but only a bit more than starting it on a flat surface.
One thing you may consider since you live in the valley is to use an electric pump and a constant circulating system.
This way there is always fuel flowing back to the tank, and your fuel will stay a lot cooler.
It helps a ton on the hot days. (Especially with an Edelbrock carb and Ethanol fuel)
Edelbrocks have smaller fuel bowls, and heat soak is a real issue with them.
Even if you don't run an Eddie carb, it makes a big difference for vapor locks and fuel boiling on hot days.