Absolutely nobody in cosmology takes seriously the notion that the Universe might be bounded. What would the boundary be? And if there is a boundary, what’s beyond it? Even if it’s finite, it’s surely still unbounded (possibly like a sphere, possibly like a torus or some other topological configuration).
If it’s infinite, then it has always been infinite. Never would it have gone from finite to infinite, just as your intuition suggests. We had a thread on this this past fall.