I think you've got the right idea.  It looks like Mike starts with alternate outside picking on the first 2 notes, then a quick economy sweep (up on E, down on B, down on E).

I tried it & find it easier to start with inside picking (down on E, up on B), but then I switch to outside as a natural consequence of trying to stay with mostly alternate picking.

But that's all due to how I developed my technique, mostly doing alternate picking starting with a downstroke.   I only do economy with straight sweeping & when I'm mixing legato lines.

I have a whole series of tutorials on developing speed, alternate picking & legato.

Speedy Ideas 1
https://www.guitartricks.com/tutorial/287/

Speedy Ideas 2
https://www.guitartricks.com/tutorial/928/

Speedy Ideas 3
https://www.guitartricks.com/tutorial/929/

Speedy Ideas 4
https://www.guitartricks.com/tutorial/973/

Speedy Ideas 5
https://www.guitartricks.com/tutorial/980/

Hope that helps!