Walnut and pore filler

Nearly every factory built table top uses a pore filler, so it's pretty typical to use. Most any commercial brand of filler will work, and application instructions are everywhere, so you can google it or look on youtube. The idea is to stain it dark, thin it to apply if needed, scrub it into the pores, and wipe perpendicular to the grain with a course cloth. Let dry and sand smooth. Apply finish, and then rub out with various abrasives to a fine polish.

If a mirror smooth surface is your objective, then a filler is probably the fastest way to get there, but be prepared for the polishing process.

There are a number of YouTube videos on how to use paste wood filler. Also here is some pretty good info I got just "googling" how to use paste wood filler. Hope it helps. http://www.am-wood.com/finishes/filler.html

You definitely do not want to apply a finish over filler that is not completely dry. My rule is to wait at least three times the drying time listed on the can. I want the filler completely dry all the way down through the pore.

I don't trust stain over a pore filler.

You always can fill the pores with poly.

The quickest and easiest pore filling technique is to use Timbermate black walnut color matched grain filler from Woodcraft, et al. An alternate method is to wet sand with BLO creating a slurry, wipe/squeegee across the grain, and resand after the BLO has cured. Both will work well but the Timbermate goes a LOT quicker and is pretty much foolproof. I use a credit card to apply and remove excess. It dries very quickly and sands easily.