It was good with other host or with same host, but fortunately the host given problems and from their onwards it went 0 in traffic from Google. This time I switched to another host and looking forward to gain domain authority and trust.
I will certainly want google to index my website. who wouldn't? Its the biggest platform for website owners to make their website visible to people. I totally agree with @Jason that strong domain authority and good backlink profile plays very important role in ranking of any website.