Welcome and thank you for sharing a wonderful heirloom! I think Kathy is spot on with ID.
1950 Martha Washington.
There is a product out there called "NOVUS 3" (check ebay) for polishing scratches out of acrylic watch crystals. It is relatively inexpensive (much less than parts & labor at the jeweler) if you are motivated to do it yourself. Put a dab on the crystal and rub it vigorously with a cotton ball, keeping it moist with solution, and use pressure. It won't affect the watch case, but keep it away from the diamonds so you don't have to pick the dried residue out of the mounts (toothpick or toothbrush). Finish by buffing with a soft cloth. It takes patience and a little elbow grease, but works wonders. I have removed some pretty deep digs myself and made many watches much more presentable without crystal replacement.