My website has been returning a 403 error for a very long time as it was still under construction.
It's online now, so I wonder: is it harder to get back in the search results now? Will Google crawl it less often because it returned a 403 error for some time?
If it helps, the website has been returning a 403 error for about 5 months.
I'd say that once you submit your sitemap and request a recrawl then Googlebot should start crawling and indexing again as you hope.
From our point of view, once we're able to recrawl and reprocess your URLs, they'll re-appear in our search results. There's generally no long-term damage caused by an outage like this, but it might take a bit of time for things to get back to "normal" again (with the caveat that our algorithms change over time, so the current "normal" may not be the same state as it was before).
https://productforums.google.com/d/msg/webmasters/V4eCCsMT00w/AZIeEMG2eEcJ
Submit a sitemap using Google Webmaster Tools and make sure that your site is fully available and works well. You should see Google fetching your site almost right away (it actually may be a day or two or three) and it should begin showing up within the index fairly quickly.
However, it will be treated as if it were a relatively new site. It is all about trust. While you may be trust worthy (I will vouch for you- who do I call?), trust for a site goes deeper than that. Any site that has technical issues for a while takes a bit of a significant trust hit.
Google thinks, "Can I trust presenting SERP links to a site that has been offline for so long?" Remember, its all about user satisfaction for Google users more than anything.
Since trust is a foundation set of metrics, it will take time for your site to be fully trusted again. For this reason, Google will present your site in the SERPs rather cautiously and it will take some time to gain in the ranks. As an example, I had a 1 week outage in Aug/Sept time frame and I have only just recovered just over half of my search web traffic. This with fairly significant PageRank, site age, and excellent speed and reliability history for 14/15 years.
Remember that search engines are rather slow. But do know that Google will fetch and index your site rather quickly, it just may not perform as you would like for a while. But focus on trust issues and creating a kick-*** site and you will be fine.
