If you can get access to the underside of the counter in the area of the crack, I think it can be repaired structurally but the crack will probably be visible; is this OK?
From the photos, you have access to the edges of this countertop, and this may be enough to repair this. The repair needs to be able to stand bending stress.
You can measure the volume of the piece by submerging it in water, and then weigh it, and compare the measured density with that of marble [2563 kg/cu.m, give or take some].
A candle flame is 600°-1400°C; you could apply that to the underside at an edge. Marble should be unaffected.
If it's some composite material, machining instructions supplied by the manuf. would be helpful.
By default you could try epoxy but the repair won't be able to withstand a downward force.