Start with a Remarketing campaign only for this first month until the pixel has picked up enough matched users and conversion data in the performance history. As a side note for e-commerce you can do Dynamic Product Remarketing which pulls products from the feed much like a Google Shopping campaign.
Keep in mind that Remarketing campaigns will not be able to spend much ad budget because the audience is made up of a percentage of people that visit your site (Facebook isn't able to match 100% of site visitors back to Facebook users). Start off with $5-$10/day for this campaign and adjust from there based on the frequency of the ads being displayed.
Once you have a good audience size and historical data then you can create a lookalike audience form your existing converters and show proactive ads to that cold list in order to build awareness.
People tend to view FB ads and then convert without clicking in FB. This can happen with Google to but it is more common with FB so it's hard to directly attribute sales and judge the performance of FB campiagns. Some of the people who convert on FB might be the sample people who are converting from an ad on another platofrm like Google. Without an attributuion tracking model it is impossible to know the exact path of conversion.