Do you have a club? You can promote it in your own club.
In other clubs, you should ask the admins first. It would be highly unlikely to be approved in a club run by chess.com, but some other admins may allow you to advertise in their club, perhaps in exchange for something (such as allowing them to advertise in your club, or otherwise helping their club).
Daily tournaments also have an invite feature that you can use to send a limited number of invites to specific people. Look at some other tournaments to find people who have participated in tournaments and so might be interested.
And once you get enough people signed up, your tournament will move up the list and more people will start to find it on their own.
Also... sometimes you just have to accept that sometimes there are more people who want to run tournaments than there are active tournament participants to fill all those tournaments, and so sometimes some of those tournaments just won't get much attention.
I have organised a daily tournament which starts on Christmas Eve but the problem is: not many people are joining it, and I want nearly 200 people to join it! Unfortunately, I can't post the link of it in the club or it would break the rules of advertising. How can I make this tournament popular? Let me know in the comments.