How as an individual can I know if the Earth is a sphere or a flat disc? What experiment can I do that doesn't involve trusting information from a 3rd party that would prove what the geometry really is?
Here is a simple experiment:
Buy a good, expensive drone. i advice you something like mavic pro.
unlock all the altitude limits and launch near a seaside.
when it reaches above 2 kms, try to check the sky line. you will see that it is curve. if you can reach over 3 kms, you will see the curve better.
You can also record it as video so whenever you think that earth is flat you can watch it again and remember that it is not possible.