our website...is a single page application and the urls change dynamically based on search results....Last week we submitted about 10 static pages which showed up at site:example.com but now they are not showing either. What shall we do so for google to start indexing our website?
You're confusing google
You're basically asking google to index your page, and then shortly after, the contents of the page change because of a search someone performed. One policy google has in terms of indexing a webpage is that it must not participate in cloaking which is what you're effectively demonstrating with your one-page dynamic setup.
See https://support.google.com/webmasters/answer/66355 for more info on what cloaking is.
Your solution is to make static pages. and when making the search engine, have the form submit to a script (that you can't expect google to index) then the script can redirect the user to the correct static url.
Say your main search engine page is at http://example.com/search and say your search processor is http://example.com/search.php.
Assume you also have these URLs:
In the http://example.com/search page, you'll have a form that will submit the user query as a parameter to http://example.com/search.php once the submit button is clicked in it. Then if the user types in the correct keyword, the script will redirect the user to the relevant URL.
For example, if the user typed in "winter tires" or "wheels" or "something black and rubbery" then you could have the script redirect the user to http://example.com/query/tires
The advantage to this is that each individual query page as well as the search homepage is static and therefore can be indexed by google because the content within it will never change (unless you determine the old article about tires or whatever is completely incorrect and/or outdated).