No one tell you this legit method man. If the first one is authority and legit for years you can;t outrank that one easily. if your ecom site is in 2nd position that means you still get sales. right?
So in that case, if I were in your position what I'm doing is spend some percentage of my earnings and reinvest those to create google ads (let's say 50%). it will rank my website above the 1st competitor. Now I get his sales. With this trick I get more visitors now. I give more features to my website. more coupons, more benefits, more value adding products for easy prices. And attracting more customers to my ecom website. it's not always win SEO guys man, just need to do some hacks like that. We are dealing with peoples thought and emotions, not with SEO. Understand that first when doing ecom website.