I actually agree with your teammate (moreso than you, anyway). You now have a single entry point with multiple exit points in your code, which is clearly halfway to spaghetti (even if you think it's warranted).
Your gripe is about indentation being too much to bear, which is a pretty superficial thing to complain about, and it's not even clear what your complaint about it is/why it's actually bad. It's just indentation... you can live with that imperfection on your code. It's not the end of the world. I know I'm a pretty happy developer whenever I can reduce other problems to mere indentation (which I can, explained below).
To me, every level of indentation actually conveys useful information: it tells me "hey, here's yet another precondition for this line of code", and crucially, it tells me that information at that line, without me having to keep scrolling up the function and then mentally negating the early-return condition to figure out what the precondition is. That's incredibly useful on its own. So many fixes & simplifications result from merely noticing "hey, this function has 3 preconditions, but I thought it should only have 2... what's going on?" And yet that's not all.
Beyond that: Not having early returns means there's a single entry and exit point for each procedure. That is also incredibly valuable in its own right. Try adding a simple print()/log() statement before the function returns when you have like 6 early returns in the function. At best, you remember to do it, but it's a ton of duplicated (and bloated) code, and your maintenance work just got 6x harder, and you have to keep them all in sync as the code grows (so it's greater than 6x harder). At worst you just miss half of them (or someone who adds another early return forgets to do any final steps beforehand) and now you introduce a bug. And on top of all that, it's so painful to leave a breakpoint and then realize a while later that it wasn't getting hit in every situation you expected, because there was an early return in the function that you didn't notice.
I could go on, but all this because there's "nothing worse" than some extra indentation?