The game opens with the same spiel as it ends: "Subject: Alyx Vance, yada yada", etc. It's all clearly G-Man's work. But the fact that it appears at the onset of the game, and has been updated by the end indicates something to me: this entire game was G-Man's gambit. And not just G-Man as he was in Half-Life: Alyx, because this incarnation is clearly aware of the events of Episode 2. Potentially, he has some degree of foresight, or might even experience time in a non-linear fashion. Either way, the whole of Half-Life: Alyx is G-Man "scouting" Alyx to determine if this specific incarnation of her is going to be good enough to replace Gordon, given that in five years' time, Gordon will be plucked from G-Man's grasp by the Vortigaunts.
So, why does this game take place five years before Episode 2? Why didn't G-Man offer Alyx the chance to get Eli back then instead of before? Why doesn't she remember this opportunity to change the future in Half-Life 2 and onward? Simply put: the events of Half-Life 2's episodes, and possibly Half-Life 2 itself were a gambit to put the Combine in a position where they'd be weakened, Gordon would serve his purpose, and most importantly: Eli Vance would die. Because with the Combine weak and Gordon no longer subservient, the G-Man would need a new agent to do his bidding. Who better than the woman who, against all odds, fought alongside Gordon almost every step of the way, to the top of the Citadel and back?
Alyx in HLA is emotionally distraught. She's constantly terrified for her father, and his multiple brushes with death leave her terrified of the idea of losing him for good. This makes this younger, more brash incarnation of Alyx more susceptible to the manipulations of the G-Man than an older, wiser Alyx (with the guidance of Gordon and the warnings of her father of the G-Man).
In other words, G-Man picked this point in Alyx's life to "scout" her as "talent", as this is where she's at her most emotionally vulnerable. When offered the opportunity to reverse her father's inevitable death (which it's implied Eli knew was coming in Episode 2), she takes it without considering the consequences of such brash actions. A mysterious man who the Combine locked up in a vault offers her the chance of a lifetime, and doesn't detail what he expects in return.
No wonder Eli is losing his mind over Alyx's sudden disappeared by G-Man's hands at the end of the game. He knows his death was coming, and when his would-be murderer was instead a charred grub on the floor, it became immediately clear to him just how long G-Man has been playing his family like a fiddle.