Time Machine

Let's play Magic: the Gathering with time travel. There are different versions of time travel to work with, so let's go over the choices.

Time Machine Assuming No Parallel Dimensions

In this version, we'll use a time machine. This is the type of time travel seen in Terminator. Back to the Future allows for parallel dimensions, so this isn't an example of Back to the Future time travel. The deck will start with a time machine artifact, equipped with the ability to travel though time while carrying capacity. To simplify things, the example will begin by using a single creature capacity time machine.

You know that at some point in the game, you're going to time travel. Let's say that that point is point p. You start a game at a point p - t_before and you'll end it at point p to p + t_after. Time traveling back in time is harder than traveling forward, because if you travel back in time, you must have the original creature and vehicle do so in the future for you to have been in the past in the first place.

Traveling Back in Time

Let's say that you want to travel back in time. Nobody can win the game until your original creature and time machine are crewed and travel back in time. To keep things simple for now, let's say that time moves in turns, so you can time travel to the start of any of your previous turns. A special token copy of your time machine and anything inside of it will phase in, seemingly out of nowhere. They will not enter the battlefield, for they will already have in the future. Additionally, they are treated as regular cards, unlike tokens. They can move zones, etc. In the future, you know the past, so you'll be able to pick sometime for your time traveler to leave.

Now, you'll have the creature from the future, but don't think that you've solved the equation just yet. Getting back an instant win condition won't do anything for you as you can't win unless you traveled back in time from the future in the first place. In fact, if you end the game for any reason, it will be a draw. The simple solution is to play both your time machine and your creature and get your creature at some point and successfully go back in time. Just as they appeared, the machine and creature will seemingly phase out, disappearing from the game altogether. Now the game can end without a draw.

Traveling Forward in Time

This is much easier, as this flows with time. All you have to do is play your time machine and creature and travel forward in time. You must say when they are going. If the game ends before they traveled to, everything is okay, as all events would have played out as normal. If the turn that they said they would exit at is reached, then they seemingly phase in, just like before, except they aren't tokens, they're the original.

Consolidating Instances of Creatures

A creature has traveled back in time and has just watched their original self use the original time machine to travel back. The creature and time machine that just watched themselves go back in time can now be replaced with the original cards as they didn't interfere and just watched themselves go back.

Maximum Capacity

When using any time machine that can hold up to a number of permanents with restrictions, if you get a time machine with any permanents in the past, you must successfully get those permanents into the time machine in the future, otherwise the game will end in a draw.

Taking Control of Your Opponents' Creatures

Now this is getting interesting. If there is any possibility that you gain control of your opponent(s)' permanents while having the time machine, it's more than possible to get them back in time (or forward). Keep remembering that the future must happen for the past to happen, so the less likely a scenario, the more work you'll have to put into it to get it to actually happen, or else the game will end in a draw.

Traveling Back With Cards That Have Other Cards 'Exiled Under' It

I'll reiterate that the more complex the situation, the harder it will to fulfill it, but if you can get a card that enters the battlefield and impulse draws for you (for example) back in time, the draws will be available to you in the past (or the future). Use discretion.

Equipment

Same thing as above. Your time traveling cat can be wearing a commander's plate, but it'll have to have worn it into the time machine.

Time Traveling Into Different Games

Every game you play with the same deck is technically a parallel dimension, not a continuation. You'll need a machine to hop parallel dimensions for that. Theoretically, though, if you manage to get your hands on one, you can send over a friend to help out.

Entropy Inverter

When I watched Tenet for the first couple of times, I enjoyed the amazing choreography as time interacted forward and backward, but then I became curious how it actually worked. A user online made an excellent diagram to make it make sense. If you want to play with Entropy Inverters, watch Tenet first.

Instead of a time machine, Tenet uses a machine to invert the entropy of matter. This makes the matter travel backwards through time.