Hello,
Thank you for contacting Rank Math Support. We are sorry for any inconvenience this must have caused you.
If you have used the action “Google: Publish/update URL”, then Google will index your url almost instantly. Please be sure you saw a successful response from the API, similar to the one below.

To answer your second question, Instant indexing is faster than manual indexing on Search Console because it utilizes Rank Math’s Instant Indexing feature, which leverages the Google Indexing API. This API allows for faster and more efficient indexing of your pages compared to the traditional manual indexing process.
With manual indexing, you would typically have to wait for search engines to crawl and discover your pages before they are indexed. This process can take several days or even weeks. However, with instant indexing, your pages are submitted directly to Google for indexing, bypassing the waiting period. This helps you get your posts/pages indexed faster and potentially improves their visibility in search results.
However, please note that it is Google’s decision if they wish to crawl the submitted URL right away or not. It depends on several factors and one of which is your site’s domain authority.
We hope this helps you. Let us know if you have any further questions.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.