The visibility of your email address on Google depends on several factors. If your email address appears on a webpage that Google has indexed, it might continue to appear in search results for as long as that page is online and indexed by Google. However, there are ways to potentially remove your email address from Google search results:
Website Removal: If the email address is published on a specific website, you can contact the website owner or administrator and request the removal of your personal information. Once it’s removed from the site, Google will eventually reflect that change in its search index, though it may take some time.
Google Removal Tools: If the page containing your email address has already been taken down, you can use Google’s URL Removal Tool to expedite the removal from search results.
Robots.txt and Noindex: Website owners can use a robots.txt file or a noindex meta tag to prevent Google from crawling and indexing specific pages. This is not something you can control unless you have authority over the website.
Data Privacy Tools: Google’s Privacy Policy also offers options for removing PII (Personally Identifiable Information) from its results, but these requests are typically evaluated on a case-by-case basis and may require substantial evidence of privacy infringement.
Online Reputation Management Services: These services can help you manage and control your personal information on the internet through various strategies including content suppression, de-indexing requests, or burying the information under more positive content.

Ultimately, the permanence of an email address showing up on Google is not guaranteed, but the steps above can help mitigate and often eliminate its presence. If you’re concerned about the future, always think twice before sharing your email address on public forums or websites.