That really depends on how you define US, Canada, invade, and conquer. "Canada" was a series of colonies until the mid 1800s. The "United States" were declared an entity in 1776, though the USA under our Constitution did not exist officially before 1788.

Short answer, we sure did.

Long answer:

Sort of close: Not the US army, but US citizens invade actual Canada to conquer: There were a few times in the mid 1800s when small bands of Americans "invaded" Canada to oust the British Empire. One time it even involved soldiers when Van Buren sent Winfield Scott with a dispatch of troops, but that was really just to calm tensions caused by US civilians. Previous to those, it wasn't really "Canada" in the way you think of the country.

Next closest: Actual America invades almost Canada with intent to conquer: In the War of 1812, War Hawks very much supported the taking of both Upper and Lower Canada. I write more about this here: https://www.reddit.com/r/AskHistorians/comments/gcnyj8/comment/fq8boys?context=1 Basically we tried, several times, but were unsuccessful in gaining territory in Canada. It started pretty good for us, then turned bad, then the White House got burnt up in the summer of 1814.

Next closest: Not really US invades not really Canada, with intent to conquer some of it, in the Revolution. While we denied the invitation to invade Nova Scotia, as I talked about here:

When things started to get violent and Boston was evacuated by the British, the loyalist citizens that went with the military were settled in Nova Scotia. New England privateers had been raiding Nova Scotia in night raids against the state and populace, making Nova Scotia much less sympathetic to America's cause. All of this combined helped Nova Scotians to not send representatives to our first two Continental Congresses. In 1775, a small group did address Washington, asking for an invasion of Nova Scotia by American rebels. He declined to help;

August 11, 1775.

GENTLEMEN: I have considered the papers you left with me yesterday. As to the expedition proposed against Nova-Scotia by the inhabitants of Machias, I cannot but applaud their spirit and zeal, but after considering the reasons offered for it, several objections occur, which seem to me unanswerable. I apprehend such an enterprise to be inconsistent with the general principle upon which the Colonies have proceeded. That Province has not acceded, it is true, to the measures of Congress, and therefore it has been excluded from all commercial intercourse with the other Colonies; but it has not commenced hostilities against them, nor are any to be apprehended. To attack it, therefore, is a measure of conquest, rather than defence, and may be attended with very dangerous consequences. It might, perhaps, be easy, with the force proposed, to make an incursion into the Province, and overawe those of the inhabitants who are inimical to our cause, and, for a short time, prevent their supplying the enemy with provisions; but to produce any lasting effects, the same force must continue.

As to the furnishing vessels of force, you, gentlemen, will anticipate me in pointing out our weakness, and the enemy’ s strength at sea. There would be great danger that, with the best preparations we could make, they would fall an easy prey, either to the men-of-war on that station, or to some which would be detached from Boston. I have been thus particular, to satisfy any gentlemen of the Court who should incline to adopt the measure. I could offer many other reasons against it, some of which, I doubt not, will suggest themselves to the honourable Board. But it is unnecessary to enumerate them, when our situation, as to ammunition, absolutely forbids our sending a single ounce of it out of the camp at present.

I am, Gentlemen, &c.

Go. WASHINGTON.

We weren't really doing great at that point ourselves. We would soon see Benedict Arnold, one of our best, defeated by smallpox and the British in Ontario (another colony not joining the rebellion), and now a colony that never showed for the Philly conventions wanted us to liberate them while they weren't trying to liberate themselves. Of course had they sent anyone to Philly in '74 Legge likely would have hung them. One can also see reference to naval imbalance and the inability to properly supply munitions to our own soldiers in Washinton's letter...

We did invade Quebec with intent to conquer. Again, things went well. We had Gen Montgomery take troops and capture Ft St John's really easily, then go take Montreal which was undefended. After that he marched to meet Gen Arnold who had taken over 1000 men on a march through the Maine wilderness to surprise the British at Quebec City. About half quit or died and the rest attacked with Montgomery. They failed, in part from a snow storm, and suffered 400 captured as well as the death of Montgomery. Next, smallpox cut through the ranks and by the time Gen Burgoyne showed up in the spring of '76, the Americans could offer little obstruction to them, resulting in a full withdrawl.

Previous to this, not-at-all America attacked not-at-all Canada, but that's because they were French, not British and certainly not Canada. These conflicts go back to the 1680s and are referred to largely as the French and Indian Wars. The first, King William's War, and the second, Queen Anne's War, saw fighting between New England and "Canada". The third was two wars in the colonies: the War of Jenkins' Ear, fought with the Spanish over Caribbean and Florida/Georgia colonies, did not see Canadian invasion. It's brother war, King George's War, did and was almost exclusively fought with Canada (which, again, was French). The final (and proper) French and Indian War saw much more fighting between British and French, starting first in current day Pennsylvania. All of these conflicts also saw natives on both sides.

Conquering Canada was a central strategic goal during the War of 1812 for the United States, and there were attempts by radical filibuster groups for the next couple of decades as well.

For the War of 1812, though, while capturing Canada from the British was a major military goal, the decision about what to do with it afterward was undecided. There were those in the United States with decision-making power who believed that Canada should be annexed, those who wanted to trade the territory back to Great Britain for political and economic concessions, and those who thought that regardless of what they thought, the liberated people of Canada would naturally want to remain part of the United States.

So the efforts, at least in 1812, were more about Canada as leverage than it was about claiming natural resources. While the war was declared for a variety of reasons, the belief that the British were the "engines" setting Native American resistance movements in motion - led by Shawnee brothers Tecumseh and Tenskwatawa - against the United States meant that the US had an interest in eliminating the possibility of future political, military, and economic aid to the Natives on their frontiers - namely, at this time, the Great Lakes region and along the Mississippi river.

The war ended in more or less a draw, but because the British essentially backed off their efforts to support Natives in US territory, the US was able to hold a political hegemony in the continent, and it eliminated Britain as a source of military aid to hostile Natives. As the sole European arbiter in North America, much of the tension between British continental aims and American ones were eliminated, and in 1823, when President Monroe declared the "Monroe Doctrine," the policy was more or less a way to swing a big stick without the risk of hitting anything; that is, the policy was just a way to articulate the current political reality without having to do anything to prove it. I write a bit more about this in the thread linked above.

The Fenian raids in the 1860s and 1870s would be the last time Americans tried to invade Canada. But these attacks weren't really sanctioned at all by the US Government, and poorly organized. The Fenian Brotherhood was a fraternal organization set up in the US by Irish expats, whose intent was to hold the colonies (and, later, Dominion) of Canada hostage and force Britain to grant Irish independence.

Their forces had recent veterans of the US Civil War and actually had an early victory at the Battle of Ridgeway in 1866, but soon found their cause thwarted by Canadian troops, militia and authorities on both sides of the border. President Grant even had some of the ringleaders arrested after a failed raid across the Vermont border in 1870.

Fenians conspired with exiled members of the Red River rebellion and captured a Hudson's Bay Co. trading post in an unsanctioned raid in Manitoba in 1871, but Canadian authorities allowed US soldiers from Dakota Territory to cross the border and arrest them without incident.

The recent US Civil War and the Fenian raids would accelerate efforts by the Canadian colonies to unite in common defence as a country in 1867.