Wikipedia pages not indexing by Google

Wikipedia controls search engine indexing and caching for its new pages. It controls caching and indexing by adding the "NOINDEX" into new article's meta."mainspace")

How much time Wikipedia will take to approve my page and showing in Google?
Short answer: (1 day to 90 days)

The articles which are older than 90 days are automatically indexed by Google and started appearing in its search results. The new maximum NOINDEX limit for new articles is automatically set 90 days by Wikimedia foundation. Therefore your article could take from 1 day to 90 days to come up in Google. And NOINDEX template will automatically removed from new articles after the page being patrolled. The "NOINDEX" word does not work on wikipedia patrolled pages. Previously the limit was 30 days. Later it changed from 30 to 90 days.

How would i check that my article is indexed or not?
You may check it in Google by searching the Wikipedia article title. If your Wiki article is indexed by Google then definitely it would appear in Google's search results most probably on 1st page of it's search results.

Wikimedia Robots.txt file controls many pages for indexing by search engines.

How Can i See my Wiki page in Google?
There is no shortcut to make your wiki page appearance in Google. Hence i would suggest you should wait it till 90 days. The no-index tag can remove automatically till 90 days or may be earlier.