According to Doom (2016) the DOOM Marine has traveled between worlds and through time suggesting not only an inter-dimensional element to the new game's story, but also time travel.
In addition the new series seems to introduce even more 'worlds' besides the Earth universe, and Hell universe but also a former elemental plane referred to as Argent D'Nur former home of the Elemental Wraiths, and guarded by Night Sentinels. There is also reference to a Seraphim race (though perhaps they are tied to the elemental wraiths).
It is all enigmatic and mysterious but the the reference could be meta in such a way that the DOOM Marine himself might have traveled between parallel Doom universes as well, to a universe where an Earth has attempted to religiously exploit or inadvertently opened passages to hell into multiple 'worlds', if not part of a single timeline (it does seem to be one of the game's way of acknowledging the many iterations of Doom that has come before).
According to Quake Champions (and as some earlier fans theories) the Doom Marine is the same Marine from the original Doom series.
The fans further theorize that it follows Doom 64, following Doom 64's ending in which the Marine choose to remain in Hell to insure it would never arise again. In some versions of these theories the original Doom universe is parallel to the Doom 2016 universe, and that he has been pulled into a separate universe. This is likely considering that way Union Aerospace Corporation functions in both universes is very different (one a largely skeptical sciene community accidently broke into hell, the other has thrived on occult worship of hell, and it's part of the company's policies), and certain characters are very different as well (General Hayden vs Samuel Hayden).
The phrase "worlds and time" is mentioned in Doom Slayer's bio in Quake Champions. It's also confirmed one of the worlds he has visited is the Arena Eternal.
Chronologically speaking in terms of Quake canon, Quake Champions takes place before Quake Arena games.
The character's bio also includes that he was a survivor of a previous Earth invasion in another world and he carries around the rabbit's foot of Daisy which in part fuels his rage and anger against the demons. This is a reference to him being the original Doom Marine from Doom/Doom II/Final Doom/Doom 64.
The manual changes the description for the Artifacts from '...the other dimension...' to '...the other dimensions...' plural, suggesting that UAC had been exploring multiple dimensions.
There is a reference to an E-BOOK in Doom RPG that seems to suggest research into dimensional and time travel.
- Stabilization Techniques for Rifts in the Space/Time Continuum