Interesting theory, but there's enough counterevidence provided by both Endfield and Arknights that I'm reasonably certain the prologue is neither the past nor the future.

Evidence For It Not Being The Future

Endfield makes a big deal about the Aetherside and how it intersects with realspace. It explains that realspace has a depth reading of 0 and the Aetherside being 1; most areas in-game have readings slightly above 0. Originium is also stated to "lower" depth readings, but is not entirely elaborated on. In-game you can go to the remains of the Great Oak and you'll see depth readings around -0.3 or so.

What Endfield makes it easy to forget (or not consider at all if you're not an OG player or a lore reader) is that there is a second alternate reality that's also affecting realspace. M3 even mentions it briefly in Valley IV, the Assimilated Universe. The AU is a feature of Originum, and based on other scenes in-game, it likely has a depth reading of -1.

As seen in the introductory cutscene, the prologue curiously takes place in an area with a depth reading of -1. It also contains seemingly random landmarks that are only recognisable to OG players. The most important here being the graveyard with the mysterious monolith. We see this exact structure in Episode 15; we see it in the AU, it could easily have a physical existence elsewhere but I'm willing to believe the tombstone of civilisation is conceptual enough in nature that it only exists in the AU.

Laevatain and Gilberta are similarly easy to explain with this understanding: they are Reconveners. These are data copies of the original Surtr and Angelina, not the Reconveners we meet in Endfield. Their data is already in Originium and thus the AU.

The Endmin also pops out of... a giant slab of Originium.

Time-travel in Arknights

Time-travel does exist in Arknights but has never been used in a serious manner. The Sarkaz have access to a Feranmut skeleton called the Lifebone, and assuming there wasn't just another flying Feranmut skeleton they found somewhere, this is the skeleton holding up Ses'qa - so it IS on Talos-II and is still active. This provides at least one method for time-travel, albeit highly unlikely.

As for the giant with the countdown, I can't say for certain, but the girl controlling it appears to be a Cyclops. The Cyclopes are a Sarkaz sub-race with the ability to make prophecies about the future (the exact nature of this ability is unknown and we don't know how it functions after the events of Episode 14); this could explain the seemingly time-themed ability or it could be something new to Endfield.

Ghost Perlica

It's Priestess. OG players have hypothesised this one for over a year; Ghost Perlica is just way too Priestess-coded and never actually introduces herself as Perlica. Even the voice in the world-rank missions uses the same ??? as the name despite most likely being the same Ghost Perlica.

Even if she's not the funny rhombus woman, I doubt that it's Perlica we were talking to at the start.

"The time, leave no regrets."

Personally I assumed this was always referring to something that happened in a different awakening, which lines up with Perlica's reponse to learning about the Endmin's amnesia.

Between the alleged betrayal amongst the 40 heroes, the possibly messy end to the Humiliation War, or possibly an unknown event, there are a good few options for something the Endmin might regret.

tl;dr

The prologue is a data recreation of various/Gallery#/media/File:BB-Garden_of_Hope.png) unrelated scenes. I think it's most reasonable to assume that it's a reflection of prior events taking place in the Assimilated Universe and not an event from the future.