Sometimes, even in this most modern of countries, you can see America as it was in the beginning. Well, not the very beginning perhaps, but as those first Europeans saw it when they first came to the New World: vast and majestic, seemingly untouched by man.

It happened to me once in New York state, in the broad green valley of the Hudson River – arguably the most splendid such landscape on the face of the earth – which the explorer Henry Hudson, sailing in his vessel, the Half Moon, under a Dutch flag, first set eyes upon exactly 400 years ago.

And it happened again a few days ago, just after dawn in south-western Pennsylvania, before the sun had burnt away the mists from the folds of the Appalachian mountains, whose low crests seem to stretch away for ever.

This was the country through which Major-General Edward Braddock marched in 1755, on his way to one of the most comprehensive, if relatively obscure, defeats suffered by British arms. Today cars and trucks roar past the monument which houses his remains, a tiny patch of imperial England next to US Highway 40. Turn towards the hills, however, and you are transported back to pre-colonial times.

Both Hudson and Braddock had their faults. Hudson was a brilliant navigator but a brutal taskmaster, a man who allowed nothing – least of all the normal human emotions of his crew – to stand in his way. Braddock, by all accounts, was a brave soldier, but a commander blind to the reality that the local Indians, who were allied with the French enemy, might be more than a match for his well-ordered redcoats, unfamiliar with guerrilla warfare in the forest. And both of them came to very unpleasant ends.

Yes, Henry Hudson had a hand in the foundation of a city that shaped world history when he came upon the place the Indians called Mannahatta, or "island of hills". Quickly, Dutch fur traders set up in the Hudson Valley, and by 1621, the colony of New Netherland had been established, followed in 1625 by the village of New Amsterdam that one day would become New York City. But Hudson considered the journey a failure, in that he had not discovered the fabled Northwest Passage to the Dutch spice islands of the Orient.

So just a year after staking a claim to Manhattan island, he was back in North America in another attempt to find a maritime shortcut to the Pacific. What proved to be his final voyage in 1610 took him even further north, into what is now Hudson Bay in northern Canada. Sooner than expected, the ice closed in and Hudson's ship was trapped and forced to winter there. The following spring, his crew wanted to return to England, but the unrelenting captain would have none of it. In June 1611, they seized him and the handful of men still loyal to him, and set them adrift in a small boat, never to be heard of again. At least, that was the version of events given by the survivors when they were tried for Hudson's murder, although there is some evidence that he was killed on the spot. However, no one was convicted or punished in any way for the mutiny.

As for Braddock, he was dead less than five months after arriving in North America. On 9 July 1755, Braddock's army of British and American colonialist troops was taken by surprise by a smaller French and Indian force as it marched to recapture Fort Duquesne (now modern Pittsburgh) and routed at the Battle of Monongahela. Some 900 of his 1,400 men were killed. Braddock himself was mortally wounded and died four days later. To avoid desecration by the Indians, his body was first buried under the road in an unmarked grave, a few yards from where the monument now stands. In charge of the burial party was a 23-year-old Virginian with the rank of Lieutenant-Colonel, named George Washington.

Today both Hudson and Braddock are remembered everywhere. The majestic river, the vast bay and various towns and townships that bear Hudson's name are eternal consolation for his miserable end in Canada's icy wastes. This year, New York is celebrating the quadricentennial of his arrival, and for eight days last month, a flotilla of small ships retraced the 120-mile journey from Manhattan island upstream to Albany, the site of the state's capital where the river became too shallow for the Half Moon to continue. The city's 4 July fireworks display last weekend was held on the Hudson, instead of the customary East River, while state wineries are issuing a special 2009 vintage.

The reminders of Braddock are less imposing, but no less numerous: the monument itself, of course, with a plaque from his old regiment, the Coldstream Guards, and a host of inns, restaurants and motels in Pennyslvania and Maryland, scattered along the fateful route travelled by his men. Various stretches of highway are named after him, as well as the river town of Braddock, the actual site of the battle, a few miles south of what is now Pittsburgh. In the late 20th century, this Braddock has suffered a second, slow-motion catastrophe, ravaged by the decline of the local steel industry that has cost it 90 per cent of its one-time population.

But in these parts of New York and Pennsylvania, the recent past soon yields to a more distant, epic past. That verdant landscape where Braddock fought and died may not be quite what it seems. The original forests were largely cut down in the 19th century for logging and fuel for the old iron smelters and to clear land for farming. But now the thick woods have returned. In the cool stillness of a summer morning, the place must look much as it did on that bloody July day in 1755 – just as the Hudson Valley, mist-shrouded and primeval, can have barely changed in the four history-crammed centuries since Henry Hudson first set foot there.