Humans alive today not being a random sample can be a valid objection against the Doomsday argument but not for the reasons that you are mentioning.
You seem to be suggesting something along the lines of “Given that I am at the beginning, I cannot possibly be somewhere else. Everyone who finds themselves in the position of the first humans has a 100% chance of being in that position”. However, for the Doomsday argument, your relative ranking among all humans is not the given variable but the unknown variable. Just because your ranking is fixed (you could not possibly be in any other position), does not mean that it is known and that we cannot make probabilistic statements about it.
Humans alive today not being a random sample can be a valid objection against the Doomsday argument but not for the reasons that you are mentioning.
You seem to be suggesting something along the lines of “Given that I am at the beginning, I cannot possibly be somewhere else. Everyone who finds themselves in the position of the first humans has a 100% chance of being in that position”. However, for the Doomsday argument, your relative ranking among all humans is not the given variable but the unknown variable. Just because your ranking is fixed (you could not possibly be in any other position), does not mean that it is known and that we cannot make probabilistic statements about it.