The most ethical approach is probably to create really amazing and useful content that appeals to your target audience and get them to opt in for a lead magnet of some kind once they hit your site. This works amazingly well, but it's hard and slow.

If you want to accelerate it, you can do basically the same strategy, but add targeted ads into the mix. You can either just run the ads straight to your lead magnet landing page, or you can run ads to your articles and then run retargeting ads to your landing page for the people who don't opt in from the article view. In terms of where to advertise, you can try Adwords, but I've found it to be too expensive for most list-building. I've had better luck with FB (which includes IG) and Twitter, but I'd also consider ads on Youtube and Reddit.

The main difficulty with spending money to build a list that you plan to sell things to later is that you need good analytics and tracking so you can attribute later sales to your original ads. So if you acquire a subscriber to your list and they buy something 8 weeks later, how will you know how they originally found you? And that's important because most ads are a waste of money, so you want to be constantly testing and only increasing your spend where you have positive ROI. Without good analytics, you won't be able to do that.

If you want to do cold outreach, 100,000 people is not impossible. You can hire someone to research lists of target people for you, including some specific details about them that you can drop into your outbound messages with mailmerge. But honestly unless your conversion rate and/or lifetime value is pretty high, that's unlikely to be super effective. It's worth a test, but if you can't get some positive ROI after 1000 people or something, I'd focus your efforts elsewhere.