Comment by qwezxcrty

Yes, but even for people eligible for EB1A (it usually has a higher bar in practice, EB2/NIW is easier but way worse backlog), filing a (or according to some lesser stringent interpretation, having an approved) I-140, will make you have immigration intent and thus illegible for extension of any nonimmigration visa.

So you apply for green card and if you don't immediately get it (particularly because of the backlog for some countries), you have to leave the US.

(I'm not an immigration lawyer and these are only my personal interpretation).