Sorry to be boring, but I've always found that "opening paragraph" does the job. Typography books often describe them this way too. Never seen a separate term.
If you call it the 'opening paragraph' rather than simply the 'first paragraph', that implies you're treating it as special or distinct, without implying anything specific about how it's written (like lead paragraph does). In any conversation about "the style of the opening paragraph(s)", it's clear what's going on.
Here's a real-world example of a typography book (Typography Essentials: 100 Design Principles for Working with Type, By Ina Salt) talking about opening paragraphs in this way, from a chapter titled "Opening Paragraphs":
THE APPEARANCE OF THE OPENING paragraph is as important as its content in drawing the reader into the text. There are a myriad interesting ways to accentuate an opening paragraph that signals the beginning of a long passage of text...
Another book example - an Indesign book with a chapter titled "First Impressions: Creating Great Opening Paragraphs" (bizarrely it then goes on to talk about nothing but drop-cap initials).
I've sometimes seen "pull-out copy" or "pull-out paragraph" used for paragraphs that deliberately break the flow of a document to stand out (like a pull quote), but these aren't necessarily opening paragraphs.