Welcome to permies Liz
I wouldn't mow first, but I'll always take the easiest way!
My main questions would be:
a) is the grass a clumping or running variety?
It's easy to find out-if you can dig out a clump things are a lot easier;
if there's a dense network of horizontal
roots, not so much
b) are there any hardcore
perennial weeds like buttercup?
If you answered 'yes' to running grass/perennial weeds, I'd
water the spot
really deeply,
put down
seriously overlapped card, then pile on all your goodies, water well and mulch.
If it's running grass, I seriously suggest not poking holes in the card for a few months,
and keeping an eye on grass incursions...forever...