I'm a little late to the party in playing Doom 2016; I got it as a Christmas gift. I loved the originals, and I still remember their plots quite well, so I was excited to play what I thought was a reboot. The beginning of the game and the "Praetor" suit immediately confused me however... it was apparently pulled out of hell but is covered in Roman numerals, serial numbers, English text (including corporate logos), and has a modern-style head-up display with English readouts -- it's clearly a product of human manufacturing on Earth. I think, holy crap, this is a sequel to Doom 64! At the end of Doom 64 Doomguy stayed in hell "forever", so they must have retrieved him.
Thinking wow, this is pretty damn cool, it's the original Doomguy, I went online to see people's reactions, but it looks like people have been arguing about this since the game came out. Reading the arguments, their sources, and looking at images spoiled the game of course. To make things worse, I haven't found a take on it that really makes sense to me, so I did my own reading, and this is the most parsimonious explanation I can think of. A timeline at the end of this post for reference (Source: Doom Wiki).
The timeline basically starts in the 2020's when the UAC established research and mining outposts on Phobos and Deimos, the two moons of Mars. There is no mention of them colonizing Mars itself -- keep this in mind. Experimental portals/wormhole technology is developed to transport resources directly back to Earth, but they accidentally connect to a parallel universe that at least strongly resembles the mythical Hell. Demons invade.
Phobos is overrun and a large chunk of Deimos is pulled into Hell. Meanwhile, demons are invading Earth and are reeking havoc in major cities. Doomguy kicks ass from Phobos, to Deimos in hell, gets really pissed about his dead pet bunny at one point, then kicks demon ass on Earth, eventually killing or disabling the Icon of Sin.
The UAC starts covering the cause of the invasion up (according to the story of Doom 64), and Doomguy suffers from Hell-induced PTSD for several years. Meanwhile, the UAC continues their cover up operation, sterilizing Phobos and Deimos with radiation. In the process they miss a surviving demon known as the Mother of Demons, a sort of "demon queen" that can spawn and resurrect demons, mutating them in the process. Another demon attack starts. Doomguy gets pulled back into service, kicks more demon ass, destroys the demon mother, and being unable to live a normal life on Earth, decides to remain in hell "forever" to keep kicking demon ass for eternity.
Earth apparently recovers over the next 70 years. I assume the UAC and the government covers the demon invasion up as some science experiment gone wrong, not an invasion from some demon realm (it was genetic experiments... or something!). Mars and its moons remained untouched until 2095. Argent energy is discovered and the UAC begins harvesting it. They discover the remains of an alien civilization on Mars in 2104, followed by the rediscovery of a hell portal in 2145. This time, the UAC tries to study Hell in a controlled, scientific way via expeditions, which led to the retrieval of the Doom Marine who remained in hell in the 2020's.
This seems pretty straightforward to me, but there are some sources of confusion, but I don't think they're really problematic at all.
1) Found demon text says the suit was made for the Doom Marine in hell by a "wretch", perhaps a demon who betrayed his kind. This makes sense of the armor's hybrid appearance: It has elements from the original Doom Marine's armor, complete with logos from the company that made it and serial numbers, but also chitinous plate segments and tubes somewhat like the armor of the mancubus (demons make chitin armor). This also explains why it can harness "Argent energy" as a power source.
2) The portals the demons use seem to be, for all intents and purposes, a form of "wormhole", a shortcut that allows for instant travel between two points in spacetime or between different universes. This is evidenced by the gore nests which show a spherical portal that connects to Hell. Any portal of this sort would necessarily connect two points in space AND time. Some of the game lore says the Doomguy traveled through worlds and time. Remember that in real life, time is relative. What this means is that hell could connect to Argent D'Nur many of thousands of years ago, then Earth in the 2020's, Earth in the 2140's, while still allowing the Doom Guy to remain in hell for an unknown amount of time, perhaps "eons", all without violating causality, because he never returns to a time before the events of Doom 64.
3) The cyborg demons seem to have a different origin than the originals, but only partially. Remember, they're not "natural" demons: they're a result of human technology being incorporated into them, both in the original series and Doom 2016. Hell in the original series is shown being a sort of medieval tech world, but the demons immediately began incorporating advanced human technology, which is why the UAC bases on Deimos looked like a hybrid of medieval tech and 21st century technology. The Doom Marine ended the invasion, apparently destroying these demons. In the 2140's, the UAC itself began experimenting with demons, creating their own cyborg forms analogous to the cybernetic hybrids of the 2020's.
4) While the demons of hell seemed to be the root of hell and demon beliefs, the night sentinels might be the source of angel myths, complete with a member of their order who betrayed them, resulting in the Icon of Sin (loosely analogous to Satan). They have a different armor style lacking any English text, and they use swords. The segments between their armor have a strange flesh-like quality, suggesting they are a different species entirely. They would seem to be another civilization that, like Mars, and like the Deimos base, was destroyed by Hell.
5) Along with the armor, another really big hint at a connection to the previous games is the dead/dormant Icon of Sin.
6) Some weapons that were prototypes in the 2020's reappear. A lot of technology may have been lost when the demons destroyed the UAC facilities, with the tech subsequently being rediscovered during the next century.
Timeline:
2018 - The military, UAC's biggest supplier, has used the remote facilities on Phobos and Deimos to conduct various secret projects, including research on inter-dimensional space travel.
2019- The Marine assaults a superior officer, and is transferred to Mars, home of the Union Aerospace Corporation.
2021 - July 1 - DOOMNL 01-D19305-1C is published.
2022 March 15 - Mars receives a message from Phobos base stating that the base under attack and requesting backup. A few hours later, the marines land and try to stop the invasion. The Marine is ordered to stay behind and protect the perimeter. The marine forces are wiped out or turned into monsters. Planetary authorities send the final Marine the new DOOMNL 01-D19505-1D replacing earlier manual (now including briefing for the Marine, and 'images from the invasion captured by remote video cameras. The video data was computer analyzed by the UAC and the results are provided "here and only here"). The Marine leaves the escape pod vowing to destroy the invasion force.
Doom Begins
Doom II Begins
No Rest for the Living begins.
Plutonia Experiment begins.
2023 (or at least a year after Plutonia Experiment TNT:Evilution begins.
The fatigued marine is decommissioned, and the military DOOM Episodes are classified. The UAC's bases are sealed, and quarantined by radioactive bombardment. Years Later
Doom 64 begins. Doom Marine is re-commissioned to stop a new threat, from a deepspace installation he once fought the Demons at. After defeating the Mother Demon, the Doom Marine remains in hell forever to prevent another invasion.
2019 - Samuel Hayden is born.
2095 - The Argent Fracture is discovered. Argent plasma was discovered in a trench on Mars by an expedition from the SS Amundsen.
2096 - The Union Aerospace Corporation established an outpost on Mars to extract Argent plasma from the Argent Fracture. 2104 (Shared with the Doom 3 Timeline) - The explorations of the caverns in 2104 led to the discovery of ancient artifact codenamed U1, the Soul Cube, along with stone tablets written by the ancient Martian civilization.
2127 - The Argent Tower is completed. 6 Months Later - Samuel Hayden transfers his mind over to a cyborg to continue his existence, after his body breaks down due to Stage 4 Cancer.
2136 - The Advanced Research Complex is completed.
2143 - The Corrax tablets are retrieved from Hell in a UAC Automated Survey.
2145 - The first Project Lazarus Manned Expedition is sent to Hell. The expedition ends with complete loss of human life, but achieved its mission. The sarcophagus of the Doom Marine is recovered from Kadingir Sanctum.
2146 - Industrial accident related deaths in the Foundry dropped significantly thanks to new UAC safety protocols where employees exposed to dangerous materials are sent to the Lazarus Labs. 351 The first Project Lazarus Tethering Operation is conducted. Pinkies are discovered for the first time.
2147 - The second Project Lazarus Tethering Operation is conducted. The expedition ends in an confrontation with the Hell Guard.
2148 - The second Project Lazarus Manned Expedition is sent to the Great Steppe. The expedition ends with similar losses. The petrified remains of a Baalgar demon is recovered.
2149 - The Argent Facility - UAC base had its last accident. October - Doom 2016 Begins.
-Edited for minor grammar issues