In general, people want to connect with people who they think can add value to their network. Even if you don't use the best outreach message in the world, if your profile says, "This person is going up in the world," people will connect with you.
In LinkedIn, the worst thing you can do is have an empty profile. The next worst thing? Having a generic one. Like, just listing roles and companies (that no one recognizes). And using generic resume things like "proven experience in bla bla bla bla" Nobody cares.
The 'easiest' way to look impressive is to have super high credibility credentials. e.g. Jezze has MIT and Google. Ana has Bucerius Law School (it's widely known in Germany as the best university in Germany).
But what if you don't have those?
I (Chiara) don't have those. I've worked mostly in small companies that nobody would recognize. Here are some tactics I've used and you can use to still look impressive. You don't need a lot. Just one to three.