Piece the top and then get some fleece for the back, perhaps a coordinating camo. or a neutral. Place them face-to-face and sew the edges, leaving a space for turning right-sides-out. (Is this what is now called birthing?) Turn, poke out the corners and stitch the opening. If the fleece does what fleece likes to do, it will stretch and want to curl up a bit to the front. Top stitch through the edges of the pieced top, allowing the fleece to look like a fuzzy binding. You can tie or tack enough to hold back and front together. The pieced top and fleece will be warm enough for the baby and you won't need batting or quilting.
I hope this is clear........