Can you post a picture of what you are doing. If test mounting the pressure plate to the flywheel without the disc in place you will have a small gap - less than the disc thickness. When you install the disc under the pressure plate and tighten the bolts it will depress the clutch plate and the fingers or arms will slightly move towards the flywheel as it's pressured up. If that isn't happening you have either some mis-matched clutch parts or severely worn out parts.
For instance, here is a picture of a Chevy clutch I was checking for uneven engagement and measuring the gap of the plate to frame around the perimeter of the bonnet or housing. You can see there is a gap - but it's less gap than the thickness of the disc which makes the whole thing work.
From memory I think the disc thickness was somewhere around 1/4" so there was about .070 to .080" of compression of the clutch plate when the whole thing was torqued down to the flywheel.