If mass/energy causes positive curvature in spacetime, and measurements of the curvature of the universe show that it is flat (or very close to flat), then is there something causing negative curvature to balance out the positive curvature from gravity? Or is this positive curvature negligible (or even infinitesimal?) when viewing the geometry of the universe? (Never studied GR or Non-Euclidean Geometry just know the basics)
As you guessed in the comments, yes, it's caused by dark energy. The curvature of the Universe is very close to zero (i.e. flat) today; there's no stipulation that the curvature has to be constant, and indeed, if dark energy continues to dominate then it may well deviate from zero. The question of why we live exactly at the point where these things are balanced is known as the coincidence problem.
For more info, see the section on the density parameter here: https://en.m.wikipedia.org/wiki/Friedmann_equations