yes you can surely find keywords with low competition, one thing you should know right now is that everything comes with a price, once you are determined to paying the price then the sky is your limit.
now for you to get very low competition kws then we will be talking about long tail kws that very few people search per month. the tool that will help in getting such kws is ubersugest.org, this is google suggest tools that brings out all the long tail kws on a particular topic.
this tool is very simple and straight to the point to use. As have said it comes with a price and lots of work.
here you are going to write articles on all the keywords you are able to gather from the tool write as many as possible that is the work in it. if you are able to do this you really do not need any backlinks to rank this very long tail keywords they just rank on their own just by the topic alone, since they are searched a few things per months that is the main reason you need so much of them.
This is the way am going right now and am getting tremendous result, note it is not for everybody but for those who really will put in the needed efforts in article writing.
In the past most of my high paying blogs got slapped by google as a result of google update hence i resulted to this methods. Give it a try by starting out with a hundred article per niche