Uh. I think the USA walked away from leading the old world order and so has less influence than it did, not more.
If we get a new world order, I suggest we think about what we want it to be before we make assertions about who ought to be in charge of it. For myself, I'd rather a world order that is not built in the image of one country, especially one that almost ditched democracy at the last election and which can't get its legal and administrative machinery to work properly.
A new world order without very large countries dominating it would be nice.
Goddamned exceptionalism.
http://www.realclearpolitics.com/video/2022/03/21/president_biden_theres_going_to_be_a_new_world_order_and_america_has_to_lead_it.html