Once you have submitted your podcast to (Apple Podcasts) iTunes, the amount of time until it will be available depends on the Apple Podcasts (iTunes) review process.
You can check the status of your submission in Podcasts Connect. If there are any errors or you have been rejected, please check the problem and resubmit. You can see a list of reasons for being rejected or removed here. (Validation errors can occur for a number of reasons such as “mismatched tags, artwork that does not meet the minimum requirements, or unescaped ampersands”. Podcasts Connect displays validation errors at the top of the new podcast page.)
Once your podcast is reviewed and approved by Apple, you will receive a confirmation email. It indicates your submission review is complete. It also includes the link to your active podcast. The podcast link is live on the iTunes Store shortly after the email is sent. Your podcast is not searchable in the iTunes Store until it is indexed, which can take up to 24 hours.