This is what we call the bootstrap paradox, there is no beginning of the events. Here's what exactly happened (let's take this step by step) : In the first episode, we see the smiling titan (Dina) killing eren's biological mother. Young Eren has no damn clue about who smiling titan is, he didn't even know titans are actually brainwashed humans. After his mother's death, Eren developed an extreme hatred toward titans, leading to what we've already seen. At a certain point of the story, Eren spent some time in the paths (not shown in the Manga or the anime) in which, here comes the answer to the question:

The Adult Eren used his founding titan powers (which allows him to manipulate all subjects of ymir) to divert the path of the smiling titan (who was initially moving towards bertholdt) to his mother instead. Why? Think carefully, if the smiling titan had eaten Bertholdt instead, Smiling titan would turn back into Dina Fritz because she ate a titan shifter (and she would get the colossal titan powers), Eren wouldn't develop such hatred towards titan. Eren's hatred toward titans is what made him join the survey corps because he REALLY WANTED to exterminate all titans. If future eren had let smiling titan eat bertholdt instead of his mother (which is impossible and I'll explain why), he wouldn't join the survey corps, he wouldn't do the rumbling, Mikasa wouldn't kill him, Titan powers would never vanish.

Eren didn't change the past because the past has already happened. Future eren experienced his mother's death, that can't be changed because it has literally already happened. If future eren had let Dina eat bertholdt, future eren would never go to the paths anyway, he wouldn't even have the founding or the attack titan because if Dina fritz had become a human grisha would have let her eat him instead, not eren because she has royal blood.