My first thought is painted quarter-round. Second choice, a thin sliver of your counter material. Is your backsplash tile solid? Might work, but then you will need and edging for the exposed top edge...

Have your fabricator do a small piece of countertop material?

Counter material^^^ is best.

2nd best would be a 1 by stick of PVC trim ripped to height of window sill and notched to fit around the jambs.

Quarter round won't look good because it isn't the correct shape to fill the space beneath the jambs.

You might need to consider putting in a deeper sill, so you can add backer board and tile underneath it. It will also fix that piece of vertical window trim on either side of the window that awkwardly ends at sill level.

You need tile there to form some type of water barrier ot that window sill will rot in no time IMO 1/4 round will just look cheap

I'm sorry, I meant a deeper window stool, not window sill or apron. I don't think a window sill will rot in no time at all. I have always had wooden window stools in all my kitchens, and much closer to the faucet than what OP has. I would not do quarter round to fix this. The following link labels parts of windows. https://www.pellabranch.com/blog/global-blogs/a-guide-to-the-parts-of-a-window/ 

We originally were thinking of putting a piece of our quartz counter in as a step. We had many problems with our fabricator (install went very badly) and we had to finish the 3rd install of our sink ourselves. We no longer can ask them for the step piece.

We considered just wood trim since it originally had a piece of chair molding there. But since we are putting tile backsplash up we thought carrying it into the window might look more continuous. Our problem lies with how to attach tile there. We are probably going to use natural marble tile.

I'm not sure what is meant by needing a deeper stool. Are you suggesting we pull the window out farther to the outside? We won't be resetting the window or the counter. Maybe you could explain this a bit more.

Thanks all

We considered just wood trim since it originally had a piece of chair molding there. But since we are putting tile backsplash up we thought carrying it into the window might look more continuous.

Don't sweat it. Put the wood back. Back prime that wood before reinstalling it if it isn't already primed/ painted.

Your window area reads as a unit, isolated from the walls. Entirely appropriate to go ahead with window trim there. A bit of tile backsplash will probably end up looking weird in that tiny space. Especially since there is no protruding window stool for the tile to die under. As is, you would have to decide on how to finish what will be a visible tile edge.

In your picture the stool and piece below the stool appear to be vinyl and part of the window frame. I thought it was installed as one piece unit. Is it not?

Our original wood window rotted on the outside and we replaced it several years ago with this vinyl one.

You cannot attach tile to vinyl, so that is another issue. If the pieces are one piece vinyl, then I don't have a solution for you.