What is the fastest way to build a large email list of potential customers that you can pitch your product to?
PS. I don't mean mass emailing people, but contacting them one by one manually and trying to get a conversation going.
The fastest way to build a list is to incentivize people to give you their email address, most commonly by offering some value for free - an ebook/guide, some tips, download of some sample, and similar.
There is nothing wrong with mass mailing people on your list to pitch your paid product, but your conversions will depend on how prepared they are to hear about it - you need to give them some value first to earn their attention. Also, mention product becoming available in the future before actually selling it - you want to generate some anticipation and/or excitement for it.
You will only have 1 shot at getting a sale from your list, so if you don't prep your audience as mentioned above, you should send your sales pitch to a small batch, so you can tweak message based on response.
Here is an excellent article from Nathan Barry about product launches (and email channel specifically).