I've put a fair amount of work into getting this exact time as low as possible for my exchange rates API [1]. I've noticed slightly better conversion each time I've taken a major step out of the process.
I've specifically eliminated some of the steps this article cites in its example of a tedious flow - for instance I changed user accounts to be confirmed by default and then only disable them retroactively if a user doesn't click the activation link within 24 hours. This way you don't need to wait for the confirmation email. Even though I use Postmark delivery times can be surprisingly variable.
I'm not sure how I could further improve the current flow, which is 1. put your email into the landing page, 2. then choose a password for your account, then 3. you're presented with an example request format including your already activated API key. Suggestions welcome!
I guess because the scope of my service is so limited it's easy to have this fast flow, no complex libraries or auth is involved.
1. https://www.exchangerate-api.com