After resawing the blanks for back, top and sides are about 5mm thick which is ways too much to build a fine instrument.
To make them thinner I use my shop made thickness sander which is basically a table which is attached to a hinge on one side and lies on a bolt on the other side. On top of the table is a metal cylinder coated with sandpaper which is driven by a motor. The cylinder lies parallel to the table and by turning the bolt the gap between cylinder and table can be varied. No rocket science, a pretty straightforward and simple concept which nevertheless works well and with sufficient precision, once you know how to use it.
Before I made that machine I use handplanes to thin the boards which took me about five times longer…
Depending on the wood and part I sand the boards to 3.7 to 2.5mm. Then I join the two halves of the top and the back and glue them together.