The voltage gain and bandwidth in opamps ARE NOT INFINITY!
The open-loop (no negative feedback) voltage gain for most opamps is about 200,000 at DC and very low frequencies up to about 10Hz.
The frequency compensation capacitor in an opamp reduces its gain 6db per octave (20dB per decade) so that at a frequency where phase shifts in the opamp would cause oscillation when negative feedback is applied, the gain is less than 1 so the opamp does not oscillate.
Some good audio opamps (OPA134) have an open-loop gain of 1 million at DC and very low frequencies. Its gain is 1 at 8MHz.