FWIW, I got API access quite quickly. Applied March 20, got access March 27. My application was only some 2 line bullshit, their example for "why do you want access" rewritten.

I applied March 16 and I'm still waiting.

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I got API access to GPT-4 almost immediately too, but I know people who have been waiting weeks. On the other hand, I don't have plugin access on ChatGPT yet, even though I applied for that as soon as it came out. There's probably quite a lot of luck involved.

I'm almost at 2 months of waiting at this point.

Strange. I applied April 6th and still don't have access

I've been waiting for over a month.