There are three time periods: before there is any intelligent life, during the spread of the first intelligent life, and afterwards where it's already extremely

There are three time periods: before there is any intelligent life, during the spread of the first intelligent life, and afterwards where it's already extremely unlikely to be independent of the first life. If you assume life spreads very fast, the first duration being much much longer than the second, and the third duration has no room for independent life to exist, it means in most universes most observers are the first. Only if a second life somehow develops during the second time window despite the expectation time being the first time window, you'll have a chance of not being the first. The time for a critical fluctuation to arise is much much longer than the time it takes for it to dominate, so most critical fluctuations are the first. Universe isn't infinite because we know it started with the big bang. We're likely the first in whatever scale it is likely that life can spread to faster than develop independently. So we're likely be the first anywhere we'll ever be able to reach.