I think the common explanation for the shift in timelines is that "In episode 1, Okabe sends the 1st D-mail, changing the world to the Alpha world line where Kurisu lives instead of dying."
However, the mail Okabe sends is just an ordinary mail (have they even invented the D-Mail yet?), it is directed to Daru, and it only contains information from the past that anyone could have witnessed. How does this message turn into a D-Mail and tip off SERN?
(Answer edited to fit what was discussed in the comments as well)
TL;DR: Whether or not the message Okabe sent is a D-Mail isn't something he has control over, at least not at the beginning of the series. The conditions just happened to be right when he sent the message that ended up becoming the first D-Mail.
First condition/coincidence:
We are told early in the story that Daru was experimenting on the microwave, having his own cellphone wired to it instead of the dedicated one, when Okabe sent him the message. It is safe to assume that he was trying to get the microwave running with its door open, because it is one of the key conditions to sending a D-Mail (learnt in episode 3), and nothing would have happened otherwise.
It has been pointed out that Daru tells us about his experiments on the microwave in the second timeline, not in the first one, which is true. However, given that the first ever D-Mail was complete gibberish and was dismissed by Daru, we can speculate that the livelihood of the group was not impacted at all by it. The only impact this D-Mail really had is:
The SERN caught on it, which eventually led to them developping a functionning time machine as well marking the start of the "Time War", and finally to Suzuha's abrupt landing on the rooftop of the conference center.
It would then be safe to assume that the group's actions, from the D-Mail being received and dismissed by Daru to Okabe wandering alone in the evacuated area, haven't been impacted at all and that therefore Daru has been conducting the same experiments on the microwave at around the same time in these two timelines. This is only speculation, but it is realistic and coherent with the rest of the story.
Second condition/coincidence:
Later in the show you learn about the second conditon for sending D-Mails which explains why they can only be sent during a certain period of the day:
The shop owner recently placed a cathode ray TV just in the right spot below their microwave. This is the reason why D-Mails weren't happening before, and can now only happen when the shop owner turns it on and it fires electrons into the microwave.
Since we assume that Daru was conducting experiments on the microwave around that time it is also safe to assume that the second condition was fulfilled, as otherwise Daru probably wouldn't have been conducting these experiments in the first place.
