This is a great question. Those things about the relationship between space and time can be really hard to understand, and I’m not sure I do, but I’ll give it a try …
I don’t think you would see the Big Bang if you travelled far enough out into space, because it’s not happening any more. But, if we could stay where we are and see far enough into space with telescopes, then theoretically we could see the Big Bang.
It’s really hard to get your head around that, but here’s why it is. Light travels at a certain speed which we know, so, by looking at the light that comes to Earth from certain objects, we can tell how long that light has taken to get here, and, therefore, how far away those objects are. At the moment, according to this website:
the furthest away thing that we can see is 7.5 billion light-years away. This means that the light from it (it is an explosion) has taken 7.5 billion years to reach us. So looking at that light means you are looking back 7.5 billion years – you are seeing the Universe as it was 7.5 billion years ago.
But we can calculate the approximate age of the Universe from the speed at which things are still rushing away from each other as a result of the Big Bang, and so we know that the Universe is about 13.9 billion years old – that the Big Bang was 13.9 billion years ago. That means that, looking back 7.5 billion years, you are looking back only just over halfway to the Big Bang. Theoretically, if we had good enough telescopes, I suppose we could see the light from the Big Bang, but we haven’t yet!
That was a really long answer, but it was an excellent question! I hope I’ve answered it!