When the oil light comes on, you have to shut the engine down immediately to prevent damage. If you did run it very long (like more than 30 seconds) with the oil light on, it's a good possibility you did damage the engine. Sadly, putting the oil in now is like closing the barn door after the horse has already run off.

Since you only bought it a month ago, if you bought it from a dealer, you could contact them. Possibly you have some recourse since you may be able to make the case that it was low on oil when you bought it. But be nice about it, because they also have a pretty good argument that it is the owner's responsibility to check the oil. If they offer to split the repair cost with you or give you a discount on some other vehicle, they're being very accommodating.

the thing is, there was still plenty of oil

There isn't enough information for we on-line guessers to diagnose your problem. Its time to stop guessing. Haul that thing into a garage and have a set of diagnostics made - this will be more than just 'pulling codes' with a code reader. If you are lucky, the only problem will be failed electronics and/or sensors. If for some reason the engine was oil starved, it could be good-bye engine, but don't panic just yet - get it diagnosed.

Did you buy it at a dealer or from a private individual? Because if there was oil in it, you have a better case for going back to the dealer. There can be other causes of low oil pressure besides extremely low oil.

Thank you all. It is with a machanic. I
guess I was just looking for hope. Got it from a dealer. As-is exactly 31 days before.

I hope you can get it fixed up and it's not too serious. Good luck.

I had several cars in my time in Europe which while not bearing a Saturn badge were no different (Vauxhall Viva, Vauxhall Chevette, Opel Kadett). The low oil pressure light came on so frequently with no cause in the end I took the bulb out. I learned to listen out for the noise the engine started to make when the oil was actually getting low, as if I topped it up every time the light came on it would be overflowing. And no, fitting a new sensor did not fix the problem but at £50.00 for a fresh engine from the scrapyard I did not really have much to lose.