You'll be lucky if the 2 ft deep hole solves the problem. To not
flood the floor, the water has to have an easier path to the sump pump
than to come into the basement somewhere else, like on the other side
of the basement. With a 2ft hole, this may work, but a hole only a
few inchs deep definitely won't, because there is considerable
resistance to water getting there from a distance away. Also, you're
going to need something to put in the hole and the std sump pump
liners are that deep anyway.
The most effective way to do this is to have drain pipe with holes
laid in a gravel base under the perimeter of the basement floor,
leading to the sump pump hole. Of course, that needs to be done
before the floor is poured.
Even before the sump pump, have you checked what's going on outside?
The fact that it happens only after a heavy rain suggests you may have
a problem with not diverting water away from the house. Make sure all
the gutters are clear and working. You have gutters right? Make sure
the grading flows away from the foundation. All gutter leaders should
divert away from the house, as far as possible. The minimum is a long
splash block, for some locations an underground routing to an
appropriate low point may also be appropriate. Go outside dooring a
heavy rain and see what's going on, if water is pooling, etc. It's a
lot easier to deal with it before it gets in the basement.