Theoretically if you were to instantly travel to another planet let's say, gazillions of light years away from Earth and can look back at Earth, will we see ourselves leave Earth or maybe even the Big Bang?

Ignoring physics entirely, as only a non-physicist can do ...

You would have to wait 'a gazillion' years for the light to reach you, so that you could see yourself leave.
You would probably not be able to even resolve our entire galaxy, let alone a spaceship leaving Earth with you frantically waving at a port-hole.
Even if you built a ginormous telescope spanning entire star systems just to gather the remaining photons that managed to get that far (probably none), why bother? (see next point)
It wouldn't even be that interesting. Firstly, think about it; why get a gazillion light years away? Why not, say, as far as the Moon? Just say you could instantly teleport to the Moon, then point your magical telescope (Hubble wouldn't even be good enough) properly and 1.3 seconds later you would see your rocket on its way. Wow! Ok pretty cool in a way, but how does doing it from the other side of the universe make it cooler?

But in the spirit of the question, yes you could.. kind of. I'm not even going near the Big Bang thing ...

Well since light does travel at a known speed, then yes theoretically you could.
There are however a number of problems you'd encounter.
You would need an incredibly huge telescope (I think) to actually visibly see our galaxy, let alone our planet (Not mentioning all the light interference and distortion etc which).
Just imagine a telescope the size of a couple of galaxies plus some...
There would also be a lot of 'background' light you'd need to remove as well, itd be like trying to find needles in a haystack except you don't know exactly what the needles look like (I think) and then piecing them all together
Since we don't know if the universe is infinite or not then you could potentially (ignoring how you got there) 'view' the initial light released by the big bang (or whatever happened then).....

You would have to travel faster than light to look back at yourself before you have left. For example, let us take 10 light years rather than gazillions. Time would still be passing on Earth when you would have left. If you would travel faster than light, you might see yourself at least leaving. Because, remember, time would still pass when you would be traveling to the other planet.

You would see neither a gazillion light years would put you well outside earths visible univers of about 93 billion light years therefore any light from earth will not have had time to reach you as light from when earth formed has only traveled about 5 billion light years so far (ignoring inflation).

You will not see the big bang either as like astronomers on earth you will only be able to see as far as the cosmic microwave background which will be at the edge of your new visible universe at about 46.5 billion light years