I mean... that's a pretty superficial reading of the situation. Where do you stop? If you assume Newtonian time, which extends back to minus infinity... well, what caused time to exist at all?
Also, no one is "lazily tossing it aside". It comes out of the mathematics that describe the observations:
Say you find that all observations you make are perfectly described by dx/dt = 1/x with current time t1. If you follow the trajectories backwards, you find that the trajectory can not be extended back past some initial time t0 at which x(t0) = 0 as the equation becomes singular then. You are now at time t1-t0 from the initial singularity. That is the age of the universe since the big bang. Now the trajectory as it approaches t0 has some unusual properties, it moves infinitely fast, etc... These might lead you to postulate that unknown physics will actually invalidate your law as you approach t0. But there is nothing logically or epistemically _wrong_ with the law you have. The finiteness of time flows out of a causal empirical induction argument. It is not introduced ad hoc to avoid some difficulty, it just is how we find nature to be at the most conservative interpretation of the evidence.
In that case, we are not disposing of any principles (as you originally claimed) when we have an uncaused first cause at t = -13.6 Billion years, instead of having at t = - infinity.
Also, no one is "lazily tossing it aside". It comes out of the mathematics that describe the observations:
Say you find that all observations you make are perfectly described by dx/dt = 1/x with current time t1. If you follow the trajectories backwards, you find that the trajectory can not be extended back past some initial time t0 at which x(t0) = 0 as the equation becomes singular then. You are now at time t1-t0 from the initial singularity. That is the age of the universe since the big bang. Now the trajectory as it approaches t0 has some unusual properties, it moves infinitely fast, etc... These might lead you to postulate that unknown physics will actually invalidate your law as you approach t0. But there is nothing logically or epistemically _wrong_ with the law you have. The finiteness of time flows out of a causal empirical induction argument. It is not introduced ad hoc to avoid some difficulty, it just is how we find nature to be at the most conservative interpretation of the evidence.