First, let me say that there is no real sandbox, it is just an imagined by webmasters who can not understand why their pages are not ranking.
Your backlinks wouldn’t have caused a penalty because that would mean anyone could use backlinks to knock out their competitors. The fact that you are indexed and getting traffic from Google is a clear indication that you are not penalized but simply ranking lower than many of your competitors.
Sounds like you need to learn the basics of SEO and begin practicing those basics. Search engines rank individual pages, not websites as a whole. The search engine’s goal is to take their users to the most relevant page, not just drop them off at your homepage and leave them there to try to find the most relevant page on your website.
You need to optimize the on-page content for those individual product pages and promote highly targeted traffic to those pages. Look at each individual page as a destination for search engine users and optimize accordingly.
You can still optimize category pages and your homepage but don’t limit your efforts there. Chances are you have a lot of serious competition for the broad categories and even more for your overall industry or niche. You are not going to get any significant traffic from those pages until you have the strength to push your way to page one of the SERPs.
Do some keyword research and find some long-tail phrases that include your base target keyword and a fair amount of traffic. Those long-tail keywords will generally be easier to rank near the top of the SERP and will begin sending traffic while you gradually work your way up the ranks for the more challenging base keyword.