Are you sure its basswood? The kit description says it's mahogany, which unlike basswood, will need grain filling. I'm not sure exactly which variety of mahogany the kits use, as it's very light and has a lot more grain pattern than the mahogany I'm used to.

But look closely at it and if you can see open pores, then you really need to grain fill it otherwise you'll never get it smooth without applying several bottles of TruOil and a lot of sanding flat.