By "his" arms do you mean his original arms or the mechanical ones?

He loses his arms and right eye during his stay on the Nevada Test Site when trying to avoid Radical-6 to be released on the air.

That happens after the kidnapping and before his trip to the moon,  so the young Sigma wouldn´t be aware of his mechanical arms, since those memories belong to the older Sigma.

Now Akane wants him to go to the Test Site again to try to avoid it. As the plot says, it will be his second time on that place, the virus spread because he and Phi failed their first attempt

Kind of confusing, isn´t it ?

His original arms

Oh, okay. No, he had the mechanical arms then.

But how? I mean I'm talking about the very first time Sigma started the AB project on the moon. How did he had the mechanical hands then?

But how? I mean I'm talking about the very first time Sigma started the AB project on the moon. How did he had the mechanical hands then?

But how? I mean I'm talking about the very first time Sigma started the AB project on the moon. How did he had the mechanical hands then?

It's a time loop for Sigma: realistically, (almost) nothing changed this time around.

Young Sigma gets kidnapped, then mindjacked by Old Sigma. Old Sigma goes to the test site to change the future, fails miserably, loses body parts, returns to the future. Young Sigma reverts to his now roboticized body, armed with the knowledge he gained from the nonary game, becomes a recluse who masters engineering and science while repeating the same mistakes Old Sigma made. Eventually he becomes Old Sigma. The nonary game is set up, he jumps into Young Sigma's body, Young Sigma plays the nonary game, learns about the future, and returns to his post-test-site body. Rinse and repeat.

The above events have likely played out several times already. Remember, even when we start the game the nonary game has been going on for a while: Phi remembers playing it, and that the game's taking place on the moon. In other words, this isn't the first rodeo. I suppose the very first time events played out Sigma may not have been at the test site/lost his limbs, but who knows? As long as Tenjimuyo is alive Akane can see what he sees, including the crappy future, so it's quite possible her first try at fixing the future involved convincing Young Sigma to head to the test site (as Young Sigma), with the idea of the nonary game taking shape after that failure. We know from 999 that Akane's not above using the brute force method of changing the future, after all...

As for your question about Clover, it's because she's a fan favorite. Nothing more, nothing less.

See, there is no "first time". He only did it one time. And he didn't do it until Akane told him to on April 13, 2029, which was after his body had lost its arms in December 2028.