Final answer:
The first landmark to be identified when performing a sciatic nerve block through a transverse popliteal crease approach is the popliteal artery, followed by anatomical structures like the lesser sciatic notch.
Step-by-step explanation:
When administering a sciatic nerve block using the popliteal approach, after placing the probe transversely in the popliteal crease, the first landmark you should be able to identify is the popliteal artery. This is an important landmark because the sciatic nerve lies close to it in the popliteal fossa. Additionally, visibility of the adjacent anatomical structures such as the lesser sciatic notch and the bony prominences of the ischium and femur may also be relevant in guiding the placement of the needle for an effective sciatic nerve block.