Added an important new page to your site? Made some changes that you really need to see reflected in the Google results urgently? There is a way to speed up the process, and it’s done through Google Search Console. What you’re looking for is the ‘Fetch as Google’ tool, which you’ll find under the ‘Crawl’ heading.
Enter the URL you want index, and click ‘Fetch’. Once this is done successfully, you’ll be given the option to ‘Request Indexing’. Of course, all this comes with the usual Google caveats that “Recrawling is not immediate or guaranteed”, “It typically takes several days for a successful request to be granted”, and “Understand that we can’t guarantee that Google will index all your changes”. But it should get things moving.
You’ll notice that you’re given the choice of ‘Crawl only this URL’ or ‘Crawl this URL and its direct links’. So yes, this does mean that if you submit an up-to-date sitemap of your whole site, then you can request Google to crawl the entire thing. Unless you’re sure that your coverage has gaps in it, this might be overkill, but it can be useful following a big site relaunch which involves many redirections. If you’re happy that your 301 redirections are all present and correct, it could be a good idea to submit a sitemap of the old site to Google so that it can follow all the updates.