What is the purpose of fame?
There is definitely a need to hype up for people on participating boards and other friendly boards, but why do things like twitch streaming and youtube? It's an audience with no investment, no familiarity and no interest in our communities. Making a view counter high is masturbation. I've been to a million. I'd rather be around 10 who care.
As for how to garner interest in participating boards and their neighbours: show them things they will enjoy seeing, that involve them. No-one likes a self-serving shill, this cup is about positive interactions and good times. In fact, part of the reason I love imageboards is the lack of advertising and clickbait and other cancerous invasive attention-grabbing of those streaming sites you mentioned.
I see the cup as an inter-community event, like the Christmas board an anon here made, like the /a/ radio streams a couple of years back. The game is arbitrary, many anons involved don't even understand nor enjoy football. It's about meeting with other boards in a chat with a theme, some pre-existing memes and a funny glitchy randomly-determined source of banter.
It's a long way to say it, but really, all we need to do is find boards that we honestly think will care, and write an honest message to them to let them know it's happening. Not some copypasta literal spam like the ICUP threads tend to be, but an organic 'Hey, there's a live event with a bunch of imageboards coming up. Come have a good time, bring some banter and cheer for your favorite boards!' And like you said, 'when the actual tournament begins'. If a board knows us and has enthusiastic people, sure, hype up the cup draw stream and rivalries. Otherwise, ask the staff a day or two before match days (on a meta board or email) if they can put a small announcement header. If a board is fast and shitposty like an /sp/ or /v/ then sure, make a thread, it makes sense, that's respecting how the board works.
A board is allowed to not care about ICUP.