olds 307 and 403

Is there fuel present when you first press the gas pedal? It really seems you have to bring the fuel from way back in the line. Also make sure a hose isn't cracked somewhere in the supply line, had that happen on my 78 Chebby truck, it acted like this.

sysmg

It's not your choke. Because it wont start with the choke practically close and after a few minutes it opens up a bit and it still doesn't start. Could be spark, or either fuel starvation (low float level or fuel pump or fuel flow to pump problem), or flooding (it would smell like gas) because of too high fuel pressure or bad needle & seat, or too high float level.