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The whole universe? Absolutely. Even the smallwst infinity is larger than any countable sum.
The visible universe, meaning those close enough that a photon could have passed from there to here since the "big bang" faded enough to allow such transmissal? I don't know offhand.
A simple web search suggest that our galaxy has less than 10^11^ stars -- 400,000,000,000 or so. ( https://en.wikipedia.org/wiki/Milky_Way )
Finding our other figure is a bit harder, since trusty Wikipedia doesn't include a direct figure and the first few articles I could find was from the BBC and used number names instead of scientific notation, which is ambiguous at this scale. ( in the long scale we only have milliardaires, and Elon Musk's brief paper fortune was a billion rather than trillion.)
Thankfully a NASA articke linked to what appears to be the underlying research paper, and gives us a helpful number of 2x10^12^. (2,000,000,000,000)
https://assets.science.nasa.gov/content/dam/science/missions/hubble/releases/2016/10/STScI-01EVSR313NHNAC17DF62MP9QV9.pdf
So, if the paper is right then, yes, there are more galaxies in the observable universe than stars in the Milky Way. But, the paper was an indirect measurement that increased the galaxy count by a whole order of magnitude, so there may be only 2x10^11^ galaxies. Except, of course, that the estimate of stars in the miky way was an estimate and could be as little as 1/4 of the number I cited above....
And if the paper is wrong and the truth of the estimate is in the middle, both of our numbers could be 2x10^11^, with approximately one star in our galaxy for every galaxy in the observable universe.
Sorry, I don't understand. Surely the number of galaxies is not infinite?
The actual size of the universe is actually not measurable. It exceeds the distance that we can observe because off the speed of light.
It might be infinite and we can never know if we measure it using light.