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?

This question has no relevance with practical world. Earth is shaped like an egg . I f you want to do any experiment , please choose
UNIVERSE as subject and tell me how vast is it and whats outside ?
If I want to take a trek across Antarctica then I think it's relevant to know if I'll be on the same planet when I get to the other side. What proof do you have that Earth is shaped like an egg? What if Earth is the centre of the universe and it's vast and the Sun (32 mile diameter according to some theories), stars and galaxies are small?