Not quite - just because an infinite variety of things are allowed to happen doesn't mean that they will. You will never have been born with all your cells suddenly swapped out for pure gold. Your brain will never spontaneously spark a fission chain reaction and detonate, in all the infinite variety of outcomes through all time. The universe as we know it will also end long before any meaningful notion of infinity applies to the possible outcomes of various configurations of atoms.
The best science can estimate, for now, is that heat death will occur in around 100 trillion years, probably closer to 1, and other universe ending outcomes can happen long before that. For the solar system, there's a few billion years before the inner planets get devoured by the sun.
In those timeframes, the only outcome you have is the one occurring now. There's no eternal endless reset waiting at the end of everything where things endlessly repeat - the number of things that occur and near infinite variety of outcomes means that even if there's a big crunch and a restart long after the heat death of the universe, there will never, ever, in any meaningfully cognizable period of time, be another universe where Earth exists, or even the Milky Way. Tiny perturbations at the beginning of time across the sum total of all particles and energy defined the state of all the things that could ever be within our universe. Across an infinity of infinities, a multiverse in which all things exist, there's no meaningful differentiation at the level of thinking about everything, so I don't think it brings anything to the table.
You get the one life - if science progresses to the point where we reach longevity escape velocity, or if they can guarantee preservation of your mind until such a time as they can revive or restore or fully emulate your embodiment, that's worth pursuing, even if somehow some weird mystical configuration of "you" traverses the eternal multiverse.
We're closing in on really weird changes in human technological trajectories, it's going to be one hell of a ride.