Digital currency, once mocked as a tool for criminals and reckless speculators, is sliding into the mainstream.

Traditional banks are helping investors put their money into cryptocurrency funds. Companies like Tesla and Square are hoarding Bitcoin. And celebrities are leading the way in a digital-art spending spree using a technology called an NFT.

On Wednesday, digital or cryptocurrencies took their biggest step yet toward wider acceptance when Coinbase, a start-up that allows people to buy and sell cryptocurrencies, went public. Coinbase shares began trading at $381 each, up 52 percent from a reference price of $250, eventually closing at $328.28. That gave the company a valuation of $85.7 billion based on all its outstanding shares, more than 10 times higher than Coinbase’s last private valuation.

Call it crypto’s coming-out party. Coinbase, based in San Francisco, is the first major cryptocurrency start-up to go public on a U.S. stock market. It did so at a valuation that rivaled that of Airbnb and Facebook when they went public.

Cryptocurrency advocates — many of whom expect the technology to upend the global financial system — are celebrating the watershed as vindication of their long-held belief in their cause’s potential.

Coinbase’s listing answers the question “Is crypto a real thing?” said Bradley Tusk, a venture capital investor whose firm, Tusk Venture Partners, backed Coinbase. “Any industry that can launch an I.P.O. of this size is without a doubt a real thing, and it’s proven by the market.”

The listing gives mainstream investors who may be wary of directly buying risky digital currencies the ability to own stock in a Securities and Exchange Commission-approved business that facilitates the transactions.

It also gives the financial world a look at Coinbase’s healthy profits — something that most other highly valued tech start-ups lack — and ballooning adoption. Coinbase, which has 1,700 employees and 56 million registered users, reported an estimated $730 million to $800 million in net profit in the first three months of the year. It brought in $1.8 billion in revenue during that period, a ninefold increase from a year earlier.

“It blows a lot of the traditional tech and finance companies out of the water,” said Jalak Jobanputra, founder of Future\Perfect Ventures, an investor in the category. “It wasn’t that long ago that people just thought crypto wasn’t big enough.”

But Coinbase’s listing also raises a question about the future of digital currency. Industry evangelists have long predicted that cryptocurrency and its underlying blockchain technology could bring about a decentralized financial system without governments or banks — a revolution rivaling that of the internet. That ethos is reflected in Coinbase’s plan to “create an open financial system for the world” and “increase economic freedom.”

But so far, cryptocurrency is mostly a vehicle for financial speculation and trading. Few people want to use Bitcoin for everyday purchases like coffee because its price is so volatile. It has also become a lightning rod for environmental concerns because its technology uses a tremendous amount of computing power and electricity.

Many early buyers have become wildly rich by simply holding their crypto or “buying the dip” when prices fall. Others ruefully relay tales of the sushi dinner they bought with Bitcoin years ago that would be worth $200,000 today or the million-dollar pizza.

Coinbase eases that trading by acting as a central exchange. Before it and similar services were created, people had to set up their own digital wallets and wire money.

“Can it be anything more than an asset class?” Mr. Tusk asked. “That’s still very much up in the air.”

Coinbase eases that trading by acting as a central exchange. Before it and similar services were created, people had to set up their own digital wallets and wire money.

“Can it be anything more than an asset class?” Mr. Tusk asked. “That’s still very much up in the air.”

Coinbase’s trajectory has followed the booms and busts of the broader crypto world. Brian Armstrong, a former software engineer at Airbnb, and Fred Ehrsam, a former trader at Goldman Sachs, started in the company in 2012, when Bitcoin was the only digital currency and it wasn’t very useful or valuable.

“It was perceived as unserious or shady,” just like the early days of the internet, said Marc Bernegger, an investor at Crypto Finance Group, an asset manager in Switzerland.

Headlines about Silk Road, a marketplace for buying and selling drugs and weapons with Bitcoin until the federal authorities shut it down, and Mt. Gox, a crypto exchange that collapsed under accusations of theft and embezzlement, further tarnished the young industry.

Coinbase tried to change that. The company joined Y Combinator, a prestigious start-up program, and raised money from top venture capital firms including Union Square Ventures and Andreessen Horowitz.

Mr. Armstrong was one of the few people in the industry who seemed prepared to comply with inevitable regulations, rather than cut corners to avoid them, said Nick Tomaino, who dropped out of business school to join Coinbase in 2013.

Coinbase also persuaded well-known retailers to accept Bitcoin. “It was good for credibility when people saw you could actually use a Bitcoin to buy a mattress at Overstock,” Mr. Tomaino, who left in 2016, said. Coinbase earned money on transaction fees.

But Bitcoin’s wildly volatile price and a slow computer network that managed it made transactions difficult, and people began to see the currency as an investment. In 2015, Ethereum, a cryptocurrency network with more tech abilities, was introduced, enticing enthusiasts to build companies and funds around the technology.

Soon after, a flood of “initial coin offerings,” where companies sold tokens on the promise of the technology they planned to build, created a new boom in cryptocurrency trading. But it quickly deflated after many projects were found to be frauds and U.S. regulators deemed the offerings to be securities, requiring that they comply with financial rules.

Over the last year, day trading and a surplus of cash sloshing around in the pandemic has pushed the value of Bitcoin, Ether (the currency of the Ethereum network) and other tokens to new heights, ushering in yet another boom.

It inspired Tesla to buy $1.5 billion worth of Bitcoin and the payments company Square to spend $170 million. In March, Morgan Stanley began offering its wealthy clients access to three Bitcoin funds, and Goldman announced that it would soon offer similar access. The mayor of Miami has proposed that the city accept tax payments in Bitcoin and invest city funds in the asset.

The stock trading app Robinhood announced that 9.5 million of its customers had traded cryptocurrency in the first three months of the year — up more than fivefold from the previous three months. Venture funding for crypto-related start-ups surged to its highest-ever level in the first quarter to $3 billion, according to PitchBook.

PayPal recently added a crypto trading and shopping feature for its customers in the United States. The company was motivated by consumer interest and advances in the technology that made transactions faster. It plans to quickly expand the offering to customers around the world.

“It feels like the time is right,” said Jose Fernandez da Ponte, head of PayPal’s blockchain, crypto and digital currencies group. “We think this has the potential to revolutionize payments and financial systems in general.”

Still, the so-called revolution faces some challenges. Coinbase has sometimes struggled to keep up with demand, with some customers who lost access to their accounts complaining that the company has been unresponsive. It has also received criticism for its treatment of female and Black employees.

Treasury Secretary Janet L. Yellen has threatened harsher regulation of the currencies, including limiting their use.

And a big drop in prices could again send speculators fleeing. In its financial prospectus, Coinbase warned that its business results would fluctuate with the volatility of crypto assets, “many of which are unpredictable and in certain instances are outside of our control.”

The industry’s biggest issue — fulfilling the promise that the technology is more than just a place to park money — could take another decade to play out.

“There’s no doubt we’re in the latest boom, and I don’t know if that’s going to turn tomorrow or two years from now,” Mr. Tomaino said. “But the busts and booms are always higher than the last.”