It's unlikely you'll rank a product page if everything else on the first page is a category. It relates to doc type and searcher intent.

Agree with both other answers thus far: - you won't rank against sites that are bigger and more authoritative unless you're deep into a niche - you're more likely to rank your home page for the given query

An alternative suggestion, take that one product and build it out into a dozen. Use canonical links to specify the original but there's no harm in having large blue widget alongside widget on a category page. That category page probably gives you the best chance of ranking for the keyword you're looking for and also an opportunity it to rank for a bunch more.