Adding value to members within a Facebook group will always pay dividends further down the road. Keep it up.
With Grace and Gratitude
Karen

If it's a Facebook group that you are talking about you probably PM them privately. You could mention your site and have them visit it when it's done. That's not considered "advertising" because you are PM" a select few not broad casting to the closed group.

Tried and true

Elaine

Thats great you are building yourself as an authority and the people that message you trust at least somewhat.

Invite them to your page amd encourage them to share your posts if they feel like they got value or learned something from it. Or if they know someone who could benefit from your post.

It's hard to give an opinion when we don't know the niche - are you saying that the closed group is a facebook group? Perhaps when you PM some of these people you could mention your site then - but when it's up and running a bit more. Surely that would be ok when it isn't posted on the wall as 'advertising'.

You are not off track, but it will require your consistency since you are still creating your site. So maintain the relationship and invite them to your site when are done.
Note: do not waste a lot of them with them. Most of the time some of them can only like your page without any click to your site.