A stretchy wrap is great for newborns since they're often too small for a normal carrier even with an insert. Some brands make ones with buckles if you don't want to fiddle with tying it on every time. I use Boba but there's a bunch of similar brands at the same price point.

I hate to recommend reddit here, but scrolling through babywearing helped me a ton with figuring out what a safe carry looks like for a tiny baby.