Valkyria stringing her bow

Especially composite bows require such careful maintenance.

This is when we are talking traditional materials, mainly wood.
With modern bows made with carbon and different synthetic materials it's not really any issue anymore.
But that would not apply to a Valkyrie's bow of course. :)

In my comment above, I meant bows crafted from horn, wood, and sinew laminated together, as described here https://en.wikipedia.org/wiki/Composite_bow

Unless this article is lying, such laminated bows are said to have been existing since 2000 years BC, though proven evidence states that the Scytians used such multi-layered bows around 400 BC https://en.wikipedia.org/wiki/Composite_bow#Scythian_bows,_bending_tips

I thought that was what you meant and I agree.

Bows have been around for more than 60 000 years. For most of the time just a single piece of wood. It seems the art has been lost and reinvent many times.

The materials need to make a composite bow was around and was used for different purposes. I see no reason why it could not have been invented even way before 2 000 BC and it wouldn't necessarily have left any archeological evidence for use to find. The factor that would have held the development back would probably be if the single piece of wood bow did a sufficiently good job during most of the bows history.

I would suspect that archery from horseback (and even from a chariot) might have been a factor than created a need for a different kind of bow than what could be used by a person on foot. But that is just an amateur speculation. I don't have any deeper knowledge on this.