Donald Trump has swept the primaries and is now the presumptive GOP presidential nominee. His primary surge — from New York to Indiana —has confounded almost all the pundits and a majority of elected officials. He understood the populist economic revolt that has been sweeping America.

It’s not just the anemic recovery under President Obama. It goes back 15 years, under Democratic and Republican administrations. The American economy has stalled. Middle-income wage earners have essentially had no pay increases since 2000. What’s more, American foreign policy has gone off the rails.

When Mr. Trump argued that America must become great again, whether at home or abroad, he hit a vein of political gold. He got there before any of the other 16 GOP candidates. This was a talented bunch — far better than anything the Democrats could produce. Mr. Trump understood that the country wants someone who puts American interests first.

So he became the quintessential political outsider. It’s what every Republican-primary exit poll showed that voters want. The people are in full revolt and will settle for nothing less than radical change in Washington, and the political system. That’s what catapulted Mr. Trump to the nomination.

Now, Trump’s critics in the GOP say he can’t win in November. They say his candidacy will lead to a crushing Republican defeat — all the way down the ticket in state after state. Respectfully, I disagree.

Though it’s early in the general-election process, a number of polls show Trump to be gaining significantly against Hillary Clinton. The RealClearPolitics polling average shows Trump only 6 or 7 percentage points back. And his general-election fight has barely begun.

All of this said, the single most important task ahead of Mr. Trump is to prove to Americans that he can do the job of president.

The people of this nation want a strong leader. They want someone who will crush ISIS. They want a fighter to sit across the table from Vladimir Putin. They want someone who can make the right trade deals with China, Japan, and Mexico. They want someone to defend the southern border from illegal immigrants and ISIS intruders.

They also want someone to bring back the post-WWII prosperity, where America grew by 3.5 percent yearly on average, and where per capita GDP — a good measure of average wages — rose to nearly $50,000 from $16,000. And where for a generation unemployment averaged 4.6%.

Knowing the two are intertwined. they want someone to bring both prosperity at home and peace abroad. Mr. Trump must convince America he can do this. He must demonstrate a firm grasp of policies — on growth, jobs, wages, trade, immigration, foreign affairs, and sound and stable money.

His serious-speech successes, teleprompter and all, before AIPAC and his April foreign-policy address, should be replicated. The economy, jobs, federal-government spending, terrorism, and immigration are the leading issues. Trump must speak to them. And when he makes his statements, he must stay on message, day after day.

I believe Trump’s America-first, no-new-nation-building, destroy-ISIS (“Their days are numbered, I won’t tell them where or how. But they will be gone. Soon.”) messaging is right on target. He has a strong economic-growth plan. He just told CNBC, “We are lowering taxes very substantially and we’re going to be getting rid of a tremendous amount of regulations.”

On trade, he needs a coherent message that rules out protectionism. In his recent foreign-policy speech he talked up negotiations. The master of the art of the deal ought to be good at that when it comes to trade. There’s no need for huge tariffs. The goal here is to tear down foreign trade barriers and make China and others play by the rules.

And rather than trade wars and currency manipulation (which includes the U.S.), the world economic system should be anchored by stable and cooperative exchange-rate policies.

On immigration, Mr. Trump needs an articulate policy that aims to secure the border and keep out illegals while letting in skilled legal workers. Voters prefer a path to legality (not necessarily citizenship) rather than deportation. And Mr. Trump — a cost-conscious business executive — must translate that into curbing the cronyist federal-government leviathan.

There are other issues. But my key thought is that Mr. Trump can win by showing a consistent seriousness of purpose and demeanor, pro-growth economic policies, and a more realistic national-security strategy. He knows, as Reagan did, that success at home leads to success abroad.

Mrs. Clinton is a weak candidate. Now Donald Trump must show that he can get the job done. He has the potential for great leadership. The whole world is watching. I believe he can do it.