Ladymatic band

Welcome @gmac51

Lovely cocktail watch, looks like it’s in nice shape. As speed said, it may be an aftermarket bracelet (if there isn’t an Omega logo on the clasp- it’s most likely aftermarket). The watch most likely came on a slim brown or black leather strap (with those turtle lugs it would have looked sharp) but daily wear on straps back then would wear them out quickly, so many went to their local druggist and bought a bracelet from the counter display.
If you like the bracelet look you can find many new and vintage that would work with it, or buy a nice strap and wear it (lots of fun color options for straps this size). You can even find a period correct buckle for it on eBay that would finish the look.
It will need a service as it’s probably been a few decades since it last got a clean and lube so you may want to see if there is a watchmaker (not a jeweler) in your area that can do that.

For what? To Get a bracelet? Definitely not. Even if they can supply you one this narrow, it will likely cost multiple times the watches value.

No, omega won’t have anything for it and even if they did it would be eye watering. Nor will they want to service it- and you wouldn’t want them too anyway (again- eye watering).

What you need to know before you go strap shopping is:
1) what is the width of the lugs (the two arms that hold the strap on either side). Usually a caliper can give you this measurement but if you have a metric ruler you can measure the width inside them (going to probably be 8 or 10mm).
2) what is the size of your wrist. A flat tape measure (like a fabric tape) can give you that. Most ladies straps are between 5.5-6.5”. If your wrist is larger, then you would want a “long” ladies strap.
3) what is the taper of the strap if any, you would want if you choose to use a vintage Omega buckle (any strap you buy will have a buckle so this isn’t an issue unless you want a vintage buckle to match the watch- just make sure the included buckle is gold to match the watch). Most of the ladies buckles were around 8mm so if the lugs are 10mm you would want the taper to be 10mm to 8mm. If it’s 8mm, then you would want a strait 8mm strap.

To remove the bracelet and install a strap requires a specific spring bar tool (most places that sell straps online will have a cheap tool for sale or included for free which will get the job done). You can find YouTube tutorials on how to change straps but if you aren’t comfortable with small hand tools and possibly scratching the watch while doing it- then let someone in a shop that sells straps do this for you.

Lastly, you need to think about how much money you want to invest in this watch. A strap can cost you anywhere from $20-200 depending on materials and quality. But this watch will (not may) need a service at some point soon. If you want to wear it occasionally as jewelry and just enjoy it for what it is, then a new strap it is and roll. But if you want it to keep time accurately and wear it more frequently- then it will need to be serviced by a professional and that can cost anywhere between $200-600 depending on where you are in the world. Despite the low “value” of these watches, they are still precision mechanical devices and the cost of service would be the same as a $$$$ watch.