I did a polyester double knit of simple squares ages ago. It had a flannel back and polyester batt and I just straight stitched down the seam lines on my old Singer. Your picture shows that your squares are on the diagonal. I would straight stitch between the squares starting at the middle corner going diagonal from corner to corner. If you can get that first long seam sewn, the rest will keep getting easier as you work your way out. If I remember correctly, my husband had to hold the bulk of the quilt as I sewed. It wasn’t easy but it is still holding together more then 45 years later. Replace any damaged squares because if it’s moth damage, the rest of that square will be weakened. As others have mentioned, you could tie it but that will be cumbersome to do also. Good Luck!