You would need to dig down 8” . Replace with type 3 hardcore 6”. Then put down 2” deep black sand and lay the lawn on that using correct artificial methods

you’ll have to add a stone layer subbas, between 50-100 mm

Hi, you will need land drains laided and going into a storm crate this is a natural soak away. The crate needs to be sett on 20mm gravel and the crate has to be rapped in terram and taped up. Land drains should be connected to the storm crate, after the trench has been dug out lay terram in first then 20mm gravel / land drain then cover with gravel and rape and tape, this way it will last for years.
Dig out 75mm off soil lay terram over the area then a fine M. O. T, and compact. You are now ready to lay your artificial grass, if you have a joints make shaw you use the correct joint tape and green glue. To pin down you can use 6in galvanised nails at regular intervals.
Top off with kiln dried sand and brush in.
Andy Fair Oak landscaping

I would 1st answer why the ground retains the rain water ?? ie: is there suitable/adequate soak away .
Then I’d take a 6/8 “ layer off the surface and lay type 1/mot road stone and compact using a wacker plate to give the ground some integrity. Then maybe a later of tarram/membrane and then lay the grass in accordance