Is it normal for blogger custom domain not to show up early in search results?

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I got a custom domain for my two years old blog. It has altogether 306 posts. I feel I did everything correct. The purchase was done from godaddy. After a few days, I went to my Google webmaster and deleted the link of the old blog. Then simply submitted the sitemap again for the custom domain. So far there has been no problem anywhere. But when I type the new name of the blog Google shows results from sites not relevant to it. Meanwhile, my own site remains missing in it. Only after several attemps Google returns me my url in the search result. Is this normal for new custom domain? Do I need to do something more to make it popular online?