You could use a piece of Baltic birch plywood that comes in 5' square sheets.

However, that ply is very light colored and it will be quite difficult to match any cherry color. Plus, any cherry wood(for use in the doors) will naturally age darker, and the colored ply will not. That creates a strange looking piece in just a couple years.

You could buy birch doors and use the same stain/dye(which will almost certainly come out a different color than the ply due to the differences in the woods used) and try to get close.

That will not be easy.

The problems in doing what you want are one reason the costs are so high.

I don't know what you $1600 quote includes but it certainly sounds pretty reasonable. I couldn't sell you a cherry window bench for $115 per foot.

It includes only face frame and top. we will have to build the boxes