OK, I'll be the curmudgeon here. Yes, it's technically possible to build what you envision. The broader issue is should you.
All the cool kids were creating similar "intro" or "splash" pages -- in 1999. The problem with them, and the reason you don't see them anymore, is that they weren't effective. They did not draw people into a site, they chased them off. Even with a "Skip Intro" link/button.
The web is an "instant gratification" vehicle. You have about 3 seconds to engage your potential user. That means something of interest to them is on-screen and viewable/usable. After 3 seconds you start losing users at a fairly prodigious rate until at about 12-15 seconds almost all are gone. Your video file will probably be multi-multi-megabytes in size. Guaranteed it won't load in 3 seconds, probably not even 12-15. "Oh, but people can click on 'Skip Intro'." Some will, most won't. They'll be hitting their browser's Back button and running away. So if you're extremely lucky, about 10% of visitors will see the opening few frames of the video then either leave or skip it. Far fewer will actually watch the whole thing -- perhaps 1%. The ROI here is pitifully miniscule.
All that is NOT to say "don't use video" or "don't use that video" on your site. Go ahead and use it somewhere, but let the user make the decision as to whether or not she or he wants to even start to load it and play it. Preferably with some warning about how large the file size is and/or how long the video lasts. Let YouTube be your guide. YouTube always states the playing time of a video and lets the user/viewer decide whether or not to play it.
Lastly, using a video as your domain's/website's opening page will kill your SEO and any hope for ranking. Search engines crave textual content. "Skip Intro" is not textual content. If that's not a concern for you, well, OK. But everything else still applies.