Mastodon has a built-in invitation system, more info about that here: https://fedi.tips/inviting-people-onto-mastodon-and-the-fediverse/
As for DMing people, you'll have to message them on other platforms because by definition they won't be on here yet.
You could for example generate an invitation link and post this on your social media elsewhere (Facebook, Twitter etc)? You can generate links that work for multiple people. That way you don't have to send out lots of messages either.