Take the air cleaner off when the engine is cold. Have someone who can start the car start it. Immediately you should see the choke plate should pop open just a bit, about 1/8" or so. There's a vacuum pod on the passenger front of the carb that is the primary choke pulloff. See if this thing is pulling in so it can slightly open the choke when the engine starts. If it is, it's something else. But most of the time it's that. Once the choke starts to warm up, the coil relaxes and it allows the choke to start opening up. This may be why after a few starts the coil is starting to warm a bit and relax. When the engine starts, the pulloff should be pulled in and stays in as long as vacuum is present.
You can also check to see if the vacuum pulloff is working even without the engine running. Just pull the rubber vacuum line off from the carb side and apply a vacuum to it and it should pull in. If it doesn't and you hear leakage, it's toast and you'll need another one.
I do not know if this is your problem since there's so little to go on and it's hard to troubleshoot over the web. What's keying me in to this as the potential issue is once it's warmed up, it runs like a top.
If it does turn out to be the vacuum pulloff, the part you will need, assuming your carb is a 17059150 (260 V8 w/2bbc, with A/C), is GM p/n 17060649. Standard part number is CPA-182, which you can get from Rockauto.com for example, or many other places that sell Standard Motor Products parts.
https://www.rockauto.com/en/catalog...164,fuel+&+air,carburetor+choke+pull+off,6000