Thirty million doesn’t go as far as you might hope in Manhattan, where it will just about stretch to a single Chelsea penthouse. But out on Long Island, where the ICC has spent its money, it’s bought two weeks’ exclusive use of all 1,000 acres of Eisenhower Park, six scaffold grandstands, two huge blocks of hospitality boxes, four drop-in cricket pitches, enough bars, restaurants, and washrooms to service for 37,000 people, and a pretzel stand. It’s an impressive set-up, especially given that it was built in six months. But then this is the city where they managed to run up the Empire State in a year and 45 days.

Apart from the up-and-down pitch, the opening game went off so smoothly that by the time it was under way the local police commissioner Patrick Ryder said his biggest worry was whether anyone was going to come down with sun stroke. ICC staff, meanwhile, were running around trying to solve a perennial American problem and find a decent cup of tea for the people in hospitality. The one thing no one had thought to lay on was a hot water urn.

The only trouble is that the ICC isn’t just paying for facilities, it’s trying to buy America’s attention too. It wants to develop new markets. Right now 85% of its revenue comes from India, and it has identified the US as the one to go for. Which figures. It already has an audience here among the south Asian diaspora, but, big as that group is, it is still only 5.5m people and they are scattered across an entire continent. Overall, the US TV sports rights market is more than 10 times the size of India’s, but if the ICC is going to get a piece of it, it needs to prove cricket is not just for immigrants.

Which is where the big set-piece game between India and Pakistan this Sunday comes in. “We had no idea what to expect,” Ryder said, “but we’re told it’s like the Super Bowl on steroids.” It is supposed to be the show that makes the locals sit up and notice.

They haven’t, yet. There was no on-the-ground advertising in Dallas, and there’s barely any in New York. On Tuesday morning the fan park at One World Trade Center was the only corner of Manhattan with tumbleweed blowing through it. England were playing Scotland in Barbados, but the big screens were off and the area was empty apart from one bored security guard standing in front of a poster with a glossary of the sport printed on it. It explained that in cricket the word wicket is simultaneously “a set of stumps and bails; the pitch/field; the dismissal of a batter”. The guard said he had “no idea what’s going on”.

The odd thing is, all this focus on winning over the people who don’t know anything much about the game means they seem to have overlooked some of the ones who already do. Neither of the two matches I’ve attended in the US so far was a sell out, and all of a sudden the organisers have announced that there are more tickets available for all the remaining games too. But then most of them are being held at 10.30am on the weekdays because, as ever with ICC events, the desire to serve the local audience is second to the need to keep Indian TV companies sweet. Even if it means there are empty seats in the stadiums.

If the USA is going to be anything more than a backdrop for Indian TV, what cricket here really needs is infrastructure and facilities. Even the chairman of USA Cricket, Venu Pisike, described his job to me as “doing the best I can with the little resources and funding available”. The Nassau County ground may not have permanent seats, but the other pitches in New York, up in Van Corlandt park in the Bronx, don’t even have sightscreens, rolled wickets, or flat outfields. In the beginning the temporary stadium was supposed to be up there too, until the local players pointed out that if it was they wouldn’t have anywhere to play this season.

“The first thing they need to do is create one good cricket field,” one local club player told me. “Even one on a par with even the worst cricket field in London. You could play for the crappiest club in London and your field is better than the best one we have in New York. We just need any kind of facility, where people can practise, nets, or artificial wickets, but there’s no grassroots investment at all.” What they’ve got instead is $30m of scaffolding and a promise from the ICC that when it’s all gone and the show has moved on, there will be an outfield with an artificial wicket left behind in Eisenhower Park.

Major League Cricket managed to develop its ground in Grand Prairie, which is also hosting games in this tournament, for $21m. They’re already developing plans for permanent venues in each of their existing host cities, which they hope will become hubs, with academies and minor league teams attached to them. The New York team hope to build theirs in Marine Park in south Brooklyn. You wonder whether cricket wouldn’t have got a lot more for its money by collaborating on a project like that. As it is, any New Yorkers who are converted to the sport in the next fortnight are going to have to travel out of state to watch another game once the World Cup is over.

Still, this is a grand project, and the one thing everyone involved in it agrees on is that it is going to take a lot of time to get right. MLC is already expanding, and its investors say its success should be measured over decades. The ICC, too, is treating this tournament as a launch. It’s only supposed to be the pop of the cork. The big question is how many people here want what they’re pouring.

• This is an extract from the Guardian’s weekly cricket email, The Spin. To subscribe, just visit this page and follow the instructions.