Where to advertise if you don't want to use social network platforms?

Newsletters are a good choice.

They have smaller, but more engaged audience.

I would start with your audience, figure out where they tend to hang out then seek advertising opportunities there.

Have you considered bumvertising?

https://en.wikipedia.org/wiki/Bumvertising

In-person: Directly in spaces where your target audience exists
Writings: Blogs, Newsletters
Forums: Quora & Reddit.
Podcasts: Feature on/Create a targeted one
Paid Advertising: not ideal in the first instance at least but a possibility
Newspapers: A bit outdated
Product Hunt: Usually good but depends on the audience and you usually want one first.

Or...

Social media (even though you don't want to, sometimes it's a must)

Where do your customers go?

Are you doing Advertising or Marketing?
Marketing is a larger umbrella that includes earned, paid and owned marketing. Advertising it paid only.

You can advertise on YouTube, Google, Facebook, BuySellAds. Not all of that is social media.

If your audience is mostly on social media you're going to have a though time.