Consider a hypothetical species living in a universe with different physics. They have unlimited living space and resources, no known existential risks to worry about, and see no evidence of other intelligent lifeforms. Their population of 7 billion is growing exponentially at the same rate as ours. The physics of their universe allow for this exponential growth to go on literally forever.
Given the doomsday argument, their mathematicians would compute the same doomsday that ours do, although their actual probability of going extinct is much lower. However, they cannot find fault with the logic of the argument.
What does this thought experiment tell us? The doomsday argument is only valid in some universes?
Your thought experiment is like saying, "suppose I win the lottery, does that disprove probability theory?" You've basically said that their total population over time is infinite, but that you've decided to focus on the very beginning of their history. A randomly selected individual from that possible world should have an immeasurably long history behind them.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.