Not necessarily, because infinity might not mean what you think it means. Infinity doesn’t mean every possible outcome occurring, because there are different infinites.
For example, you can count an infinity using 1, 2, 3, 4, 5… But you can also count an infinity using 2, 4, 6, 8, 10. The latter infinity will only include half the numbers of the former, missing all odd numbers. It’s essentially an infinity 50% smaller than the other infinity - yet both are infinities. Maybe in this example, your consciousness is an odd number?
Another way to look at it is that there’s an infinity in between the numbers 0 and 1 using endless decimal places, and none of those numbers will ever be 2. In this example, maybe your consciousness is the number 7.