Our Patience is infinite, but so is the universe, and the universe, or time-space is curved, that curve is infinite, & arrives back at the same spot as we started... here....
If it is curved and therefore closed (positive curvature, k=+1) it is BY DEFINITION NOT INFINITE!
But, all current up-to-date measurements of CMB, SNe Type 1a, Baryonic Acoustic Oscillations etc. suggest that we live in a FLAT (not curved, k=0) Universe. The CMB radiation itself is indicative of a Big Bang, so the Universe, however vast it is, is finite. The observable Universe is of the scale of 10^26 meters, but the actual Universe is assumed to be (from measurements of the evolution of it's expansion, see scale factor a(t)) at the scale of 10^30 meters. Mindbogglingly big, but still finite.