I'm experiencing something like this now. The number one site in google for a specific search term, from a specific location, has a DA of 1. It has one link to it from the web design company that created the site. My own sites homepage outscores this homepage with every tool I use.
It's good to have a high DA, but Google can punish your site for a variety of reasons. If your site is on a shared server and that server is home to some dodgy sites then you could be penalised. I assigned a dedicated IP to my site which helped a bit. My own site was for a business that was part of a larger business which had its own website. There were a number of links between the two and were initially both on the same shared server, so creating the dedicated IP helped here. I also removed all the links between the two sites and then created only one link to the other site as the original links were not really necessary.
I'm still trying to get the site to rank higher than the lower DA site so I'm sure there are plenty more things to try. It's trial and error I suppose.
If your website DA PA low, but still it's ranking on google then it may be possible because your website is new and there is no any bad linking. where higher DA site getting low ranking due to their bad quality backlink. Sometimes, Google crawler come they seen lots of new information related to a particular category then they display on a higher rank or it may be possible, you don't clear your search history or cookies so that your search keywords or website display on the first page.
Domain Authority (DA) is a search engine ranking score developed by Moz that predicts how well a website will rank on search engine result pages (SERPs). A Domain Authority score ranges from one to 100, with higher scores corresponding to a greater ability to rank. hope this will help.