"so that the sewing machine could rest on the drawer "

Not "on the drawer", because the bottom of the drawer can't hold up the weight of the machine.

What you do is replace the drawer with a solid piece of plywood, well-braced with angle brackets, to support the machine. This has to be at the right distance below the desk top to make the machine sewing bed level with the desk's top.

Then re-attach the drawer front over the opening, just for looks.

I had wondered about the drawer being able to support the weight of the machine. A strong piece of plywood makes a lot more sense. And I like the idea of replacing the front of the drawer.
Now if I could only explain this to DH

remove the drawer. separate the drawer front from the drawer. measure where you want the machine to be placed - mark around the edges of the machine. cut out that section perhaps enlarging it slightly .
glue the drawer front back on. purchase four "L" brackets. Cut a piece of plywood the same width as the opening under the desk top (not the same size the opening cut in the desk top)i.e. where your knees go. You might need to add some boards (1" x 4") to the sides of the desk where the L brackets will be attached. attach the plywood to the L brackets, attached the L brackets to the sides of the desk. you will need to determine where to place the plywood (how far below the desk top) before installing the brackets) so the machine does not rest too low

carolyn