The site is indexing okay. A Google search using " site:http://customerconnect-services.com " will give you a rough approximation of what has been indexed for this site (Google Search console will provide more accurate data, however).
But Indexing isn't your issue. In short, this site isn't ready and, I'm afraid to say, it doesn't really deserve to rank well. (That doesn't mean it can't rank well, but it needs work - lots and lots of work.)
Looking through the currently indexed pages, you will see that a few Lorem Ipsum (pages with dummy content) have been indexed (these now 404 - http://customerconnect-services.com/?p=12982 for example), this is our first indication that the site is/was recently under development.
Further, there are other signals that this site isn't yet compete: http://customerconnect-services.com/our-offerings/ - the second slider on this vaguely titled page shows a slider "CONDO Makes selling and buying easier...." This is in no way relevant and is likely a remnant from using a template site with pre-populated demo content.
While we are on this page, let's look at the Navigation label and URL - 'Our Offerings' /our-offerings - offerings of what to whom? This could not be vaguer! These elements need to be used to tell visitors explicitly what it is you do. 'App Development' /app-development or similar would much better. As it stands, the visitor is expected to click it to find out what the page might be - assuming that they're sufficiently motivated to do so. Take a look at Steve Krug's 'Don't Make Me Think' then buy every client a copy. (http://www.uxbooth.com/articles/10-usability-lessons-from-steve-krugs-dont-make-me-think/)
Look at those who are ranking well for this phrase and compare your client's page against it Here's an example (These are number one in the UK for the term 'mobile app development':
https://www.mobilesmith.com/app-development/ - not an exact match for the service your client offers (though I'm still not sure what that is) but it's close enough to demonstrate the gap between where you/your client is and where they want to be. On-page grader gives your client's 'our offerings' page a generous C for 'mobile app development' from a user's perspective, it's a F.
Then, below the slider we get:
GET FEATURED ON GOOGLE AND APPLE STORE. ENHANCE CUSTOMER ENGAGEMENT USING ANDROID AND IOS APPS
Stop. What does that actually mean? This is just vague filler - it means nothing. and you're still not telling me what you do!
The list goes on (and on), I'm afraid. And while I'm being brutally honest, the domain name is AWFUL - it is as vague as the rest of the content, it also entirely unmemorable; not the end of the world if your content and user experience is up to scratch but it isn't. (Granted, as the SEO for this client, this is likely to be out of your remit.)
I don't think I would be helping you if I were to be delicate about this, so forgive me: The site looks like a template site with some content hastily thrown into it. In essence, your client has a LOT of work to do before they can expect to see results.
The technical SEO aspects/mechanics of the site (that you reference in your question) are a secondary concern. Content and UX are your primary concern - without getting those right, you're never going to succeed. Google is better than it's ever been at sniffing out weak content, so don't expect to circumvent this with a few keywords in your content and a handful of backlinks.
Good SEO is hard enough when you're working with a well-designed and well-established site; with a half-done website, that has been (or appears to have been) hastily assembled, it's impossible.
Start (and finish) with the user in mind, give the user what they want (Google is not your user), answer their questions, deliver your message clearly and make it easy for them to engage with you and then build upon that.
I'm sorry to be so blunt, but no-one wins until these issues are tackled head-on.
As an aside, I'd run a Fetch as Google from Google Search Console to speed up re-indexing. (https://searchenginewatch.com/sew/how-to/2326164/index-your-content-faster-with-the-fetch-as-google-tool)
Good luck!