Unless you are positive that the well is under the slab, you might want to dig out in front of the steps to see if the lines go on out into the yard.
Otherwise you remove the slab to get to the well. You have a pit type well, under the slab. Remove the slab and you probably will have a cement walled box 4-5'+ deep with the well in the middle of the floor.
If you're creative, bust the wall out around the pipes and see if you don't go into a small room, under the slab.
Removing the slab shouldn't be very difficult, unless you've never done anything like that before. A couple strong ground pin type steel bars to raise it (or a backhoe) so you can get a thick walled pipe under the front edge and some way to pull the slab away from the house, rolling it on pipes. Then you roll it back when done.
You won't be able to raise the casing unless you cut a hole in the slab that can then be covered. That would also require a pitless adapter which you probably don't have now. A pitless would be a good idea and then you wouldn't have to remove the slab in the future; just the slab hole cover.