The first champagne corks were popped open at a bar next to check-in as early as 8.30am at Heathrow's bright new Terminal 2 on Wednesday. But not, as a spokesman hurried over to point out, by airport management or staff.

Caution, contingency planning and a thorough dose of public humility had marked the buildup to the opening of the £2.5bn terminal, with staff still scarred by the debacle of Terminal 5's first day in 2008. After lost bags – and lost employees – derailed that long-awaited grand opening, Heathrow conducted a review of not just T5, but every terminal opened in the last decade.

Seventeen arrivals and 17 departures on a single airline, United, were all Heathrow gave itself to handle on launch day: just 6,000 passengers, a 10th of its capacity. The first plane landed from Chicago six minutes ahead of its 5.55am slot, and passengers were swiftly ushered through immigration and reunited with their bags.

Gerard Fox, 46, a businessman from Chicago on the first flight UA958, said the new terminal was "pretty cool. Higher ceilings, a bit different. A bit curious why they had all this pageantry – beefeaters and stuff – for a red-eye flight."

Stuart Weinstein, an orthopaedic surgeon, said all the immigration desks were staffed. "Through in a minute – it's usually very laborious." As a frequent traveller, asked if he thought Heathrow needed a new terminal, he said: "oh gosh yes."

Early passengers were most delayed by camera crews. Lindsay West, from Salt Lake, Utah, said it had taken her group, in for a coach tour of Europe, an hour to get through immigration and the baggage hall, fielding questions. "It was cavernous, beautiful, well laid out – but kind of creepy. There's no one there. Just media and all the corporate types."

One such was John Holland-Kaye, the incoming chief executive who oversaw T2's development. He was up in the early hours to see the first departing passenger, in at 1am for an 11am flight to Los Angeles to claim a slice of history.

"Most of us were too excited to sleep much," he said. It felt like a chance for many staff who had lived through T5's opening to "get that out of their system", the phased rollout a sensible act of caution.

He has carried around a copy of the critical Commons select committee report into T5 – "a national embarrassment" to remind him of everything that could go wrong. Lack of parking space. Poor signs. Disoriented staff. Steps barring wheelchairs. And a new state-of-the-art baggage system, at the root of chaos that saw British Airways cancel dozens of flights.

Heathrow hasn't taken a similar gamble with T2: its solution is a conveyor belt connection to the existing machines in T1, installed and monitored by German specialists.

Six months of trials, with more than 14,000 people, kicked the T2 tyres. Bosses were clear they could never predict the random behaviour of passengers – and employees – when it was actually open.

Heathrow is seeking to mould that behaviour: departing passengers are pushed to selfservice check-in using any kiosk in the building, billed as a world first.

While 70% of passengers already check themselves in, it remains to be seen if that will work so smoothly when passengers flood in: at 6am one family from Peterborough was struggling with recalcitrant machines, even with considerable staff assistance. Andrew Godfrey, 42, checking in for a trip to Tennessee via Newark with his wife and another couple, had needed three goes to get his friend's passport to successfully scan. "It's been about half an hour – a few teething problems but it's nice and modern isn't it." They'd seen little fanfare – "I think they're saving the champagne for the Queen."

The Queen will officially open T2 (full name: the Queen's Terminal) on 23 June, giving the airport weeks to iron out any more possible teething problems. A second airline, Air Canada, moves over later this month, and by the end of the year 26 will operate from T2.

Aside from the huge Slipstream installation – a 77-tonne piece of public art from sculptor Richard Wilson – architecture critics had given the £2.5bn T2 a sniffy reception. But passengers, often rattling around often outnumbered by staff, broadly gave it the thumbs up. It may not prove the new Covent Garden the Spanish architects had optimistically promised, but it does have an atypically flashy Wetherspoons pub at check-in with panoramic views (first pint sold at 4.05am), a John Lewis store and a Heston Blumenthal cafe in the departures lounge.

Blumenthal, inspecting croissants airside, said the liquid nitrogen (for ice creams) and wood-fired ovens (pizzas) troubled security less than the blades. "The chef's knives are chained to the surface or even the walls in the kitchen ... I was moaning about it but it is an airport, it's reassuring really."

Snail porridge hunters may be disappointed. "It's democratic, it's not the [Fat] Duck. People aren't coming here for the restaurant, they're getting a plane somewhere." Although, he said, brightening, Heathrow claimed one passenger had booked flights in and out specifically to try his food.

Few would have willingly spent time at Heathrow a decade ago. But Terminal 5, once properly functioning, has garnered global accolades. The airport's bigger ambition will be that its gleaming infrastructure underpins its case for the long-awaited third runway.

"The most important argument for expansion is credibility with passengers," said Colin Matthews, the outgoing CEO, who spent his first day at Heathrow six years ago in T5 opening hell. He spent early yesterday morning away from the frontline, in Gold Command of the airport's crisis contingency plan – the man set to alert ministers if embarrassing history repeated itself. By 11am, he was in Blumenthal's, ordering a pizza.