I AM NOT A LAWYER AND THIS IS NOT LEGAL ADVICE!
I was browsing an article on Blogger Law and I came across this direct issue. Here is an example case they cited:
A leading case in the area of trademark disputes is Continental Airlines, Inc. v. continentalairlines.com. In that case, the dotcom was simply re-routing visitors to a travel site where they could purchase Continental Airline tickets plus pay an extra $15 fee to use the service. The court awarded the domain to the Airline on the basis of trademark infringement.
I highly suggest reading #5 in this page as it is an excellent answer for this question.
I would say no. You will not get permission from Google and the likely hood of confusion is high.
Here is an example:
In 1988, Quality Inns was planning to open a new chain of economy hotels
under the name "McSleep." After McDonald's demanded that Quality Inns not
use the name because it infringed, the hotel company filed a suit in federal
court seeking a declaratory judgment that "McSleep" did not infringe.
McDonald's counterclaimed, alleging trademark infringement and unfair
competition. Eventually, McDonald's prevailed. The court's opinion noted that
the prefix "Mc" added to a generic word has acquired secondary meaning,
so that in the eyes of the public it means McDonalds, and therefore the name
"McSleep" would infringe on McDonald's trademarks.
You can assume the same for YouTube as people would think it is a branch of YouTube or sponsored by YouTube.
It is not always about money it can really come down to will a user confuse your domain with the youtube domain and the answer is most likely yes.
A good book to read on Trademark/Copyright Law is Intellectual Property: Patents, Trademarks, and Copyrights by Richard Stim. Published by West Legal Studies. That book gives you a good base and is used in Law Schools and you can understand it.
The overall best bet would be to name it something generic vs a trademark.