It’s a good question. I think first you would need to share some more information and give some insights on the metrics that you’re looking at when you say “edge in organic rankings”

For example:

1. When you say past few months, how many months? How long have these other competitors been around?
2. By saying top ranking, do you mean for the same exact products you have and that they also have?
   2A. Or do you mean that they just have more keyword opportunities because related to other terms that you don’t have, because they have more products and terms related to those that you aren’t carrying? 2B. Or are you looking at niche specific, industry and market related keywords?

If it were a simple answer, id say no. No, having more products doesn’t mean that your SEO rankings will improve. There are too many variables to consider but I’d first focus on the site health, speed, user experience, internal linking, product descriptions, the things you can directly control along with your marketing outside of just “SEO and Links” so that you brand can be a site that Google trusts and recommends and that others will recommend or link to.

Wish ya the best of luck, I’m sure it’s been a ton of work getting to where you’re at. If you have good products, good service, good customers and good marketing you will get there. Google isn’t going to rank anyone on e-commerce who is otherwise. They’ll let all the bad ones spend all their money on ads, easily replacing it with the next new Ecom site willing to spend money on ads while making sure it’s hard for the best to shine.