Wouldn't make any sense documenting A-Z on how to get targeted US audience as that would take the whole day from the individual trying to do such.
My Tips would be ;
1. If your source of traffic is SEO: Although, This Niche is way saturated and dominated by authority websites. Your best bet will be getting working on long tail traffic targeted at US audience when going through your keyword research.
2. Referral: Since SEO could take your time to start seeing traffic ( Audience), I will recommend starting with QUORA / REDDIT. Pitch yourself as an expert then contextually link out to your blog when providing answers to people's questions. This approach would bring solid referral traffic if you could answer 10 questions a day for the first 10 to 15 days of launching your website.
3. Social: The least I will recommend are facebook groups related to health Niche as they always get you restricted from posting random links especially if you a new member, Are you on budget? you could build your audience around your website facebook page and they will be yours forever.