This isn't the process taking a while - the delay you're thinking of is after technical validation, while the staff check the conntent of the podcast (which of course can't be done automatically).
When you first submit a podcast you click the 'Validate' button and it should only take a few seconds before you either get the message 'Prepared for submission' and you can then click the 'Submit' button, or an error message rejecting it.
Clear your browser's cache (or use a different browser) and try again. If it doesn't behave as I describe, you could post the feed URL and I can check whether it's been successfully submitted or not (because if I try to validate the feed it won't allow it once it's been submitted).
If it's not working after that you'll have to contact Podcasts Support. Go to https://itunespartner.apple.com/en/podcasts/overview and click the 'Contact Us' link at the bottom of the page.