Oh well, whatever --- I'll just refute it again --- in short form.
The video assumes big = old --- overlooking the fact that the universe was stretched to its current size w/i a moment of time.
A light year is a unit of distance, not time, and if distance increases w/o time, then his whole premise fails.
Sorry AV, but this latest attempt fails horribly. However, I will do you the respect of explaining why... not that I expect, even if I somewhat hope, that you'll return the favor.
Let's consider the furthest galaxy that we have observed so far. It's actually mentioned in that video. By all of our measurements, the galaxy in question is about 13 billion light years away.
Now, we've got two possible options with what you proposed:
Option 1) The universe expanded prior to that particular galaxy forming. Unfortunately, this option doesn't really help your case since the measurements still place that particular galaxy at 13 billion light years away. If your explanation were true, our ability to simply see that galaxy would indicate that the "expansion" you described occured more than 13 billion years ago.
Big=old still works.
Option 2) The galaxy in question (as well as all other galaxies) all existed within a small portion of space that then expanded out. Unfortunately, the explanation doesn't really work either. But here's the fun part! There's a scientific explanation for why this option doesn't work! Ready for it?
First, let's establish that the only way for us to see an object that is 13 billion light years away, without the light from that object actually travelling for 13 billion years, is if the light we are currently seeing from said object is actually much younger than we think it to be.
Now, unless you want to try and pinpoint down the age of the universe, I'm going to go with the relatively-standard YEC-literalist perspective of ~6000 years.
Based on that, the light that we are currently viewing from the galaxy in question could only be 6000 years old. In other words, we would have to be seeing said galaxy at the position it was at 6000 years ago. Now, comparing that information to what our other measurements tell us... we have a problem. In order for this to be true, the galaxy in question would have needed to travel a MASSIVE distance in a very short period of time.
Even if THAT was possible, the resulting velocity would have caused a MAJOR doppler-shift in the light we are observing from it.
But we don't see any of that. There's no strange blip in the data... all of the tests confirm the same answer.
So... if every single method of determining the distance to that galaxy, and thus the MINIMUM age of the universe (since we can see it) shows the same result... I believe we can only form two logical conclusions:
1) The tests are right.
2) God created the universe in such a way for all of our tests to show us something other than the truth. Hence, he is the ultimate deceiver.
(Oh, and I don't mean to present a false dichotomy. If someone believes a different option exists, please speak up)