Ranking Keywords with SERP containing .gov sites

Hi SEOs

I would like to rank for a couple of keywords, but the keywords have returned results where the top 5 sites are .gov While they are not SEO optimized, (No H Tags, no links, low PA, but aged) is a new website able to outrank them?

Thanks in advance!!

Are there any Google Entities in the SERPs (those Knowledge Graph boxes that occasionally appear)? What's the quality and quantity of the inbound links pointing to the root domains of your potential competitors?

I would give it a shot, but I've never had government websites as competitors.

Hi Zwielicht, thanks for your response, nope, no knowledge graphs appeared in the SERPs... and basically if I was the user search for the long tail keywords that I'm targeting, the .gov websites wouldn't return with a satisfactory answer... I believe the gov sites are there because it is a subject that is closely related to that gov department's site.