It's fairly straightforward -- use your fountain of money from search ads plus a huge infrastructure to support it to pay the costs rather than pass them on to users.

Operate at a loss to drive out all competition and prevent new competition from arising. Increase ad obtrusiveness to drive up revenue, and every once in a while increase creator payouts to keep creators on your platform, until hopefully the lines cross and you start to make money. Maybe. Every once in a while a competitor might make a go for it, and you'll have to reduce ads or offer more incentives to creators to drive them out. Sometimes you may have to lobby the government to help you out on this.

One bonus is you can use the goodwill from your video site to drive traffic to your search engine.

If you don't have a fountain of infinite money from your search engine (or if you don't currently operate a gigantic search engine), then you might not be able to pull this off.