To make the job easier use a circular saw to cut the plywood sheet first into 2 2 8 strips which will be much easier to handle.
Reasons to put plywood in attic.
So you can put 8 inches of insulation down then put the plywood over that.
Now in your particular part of the country you re going to want a lot more insulation than that.
Stop using your attic for storage.
The plywood should be perpendicular to the joists so that a signal sheet spans multiple.
The decision regarding the thickness of plywood to use for the subfloor in the attic has a lot to do with how you intend to use the attic and it also depends on the spacing of the ceiling joists.
But if the floor is covered in plywood you can t stuff enough insulation beneath it to do the job sufficiently not even in warm climates.
Plan to pull up the flooring and layer new insulation on top of the old.
Carry a piece of plywood to one of the far corners of the attic and lay it on top of the installed boards.
So what you might want to do is sort of map out an area in the center of the attic where you have your storage and then the rest of the area you could put more insulation.