I have laid up parts greater than 7mm thickness. Yes it is possible.
The issue you will have is the first layers starting to go off before you vac bag it. That means you can have a resin rich layup. Not ideal.
Why 30 layers at 7mm? that does not make sense. Use heavier weight carbon in uni and double bias.
You could get your layers down to 10. Use 600gram insteat of 200grm weights. If you want a nice looking layer then put the 200gram twill on the outside only.
Will 10 heavier layers you physically will be able lay up the job faster and get the vac bag sucking before the resin goes off.
Preparation is the key!
Having all your cloth laid out and ready should make it quite a quick process.
I am using slow set epoxy to give me more time.