The Treaty of London has nothing to do with the establishment of the US. It ended a war between England and Spain. It did NOT settle America, nor did the Spanish - apart from the deep south coastal areas & in a very minor and unimportant way my own southwest.
And Spain did NOTHING but suck wealth FROM any place they colonized.
King Philippe I/II (formerly King of Spain AND King of England ~ he was Bloody Mary's husband) got into an eternal war with the English and with Protestantism in general.
He died in 1598. Until he died Spain effectively prevented EVERYONE ELSE from having more than a passing interest in the Americas.
After he died King Philippe II/III, his son, decided to put an end to the conflicts and get on with the development of the Americas (and though a fair share of the credit probably goes to his counselors who also worked for his relatives throughout the so-called Hapsburg Empire, we have to assign the primary credit to Philippe II/III.
I know you don't want to do that but that's because you have no interest in history.
So, by 1604 Philippe II/III had created what was called The Treaty of London (1604) and literally crammed it down the throat of all the powers who wanted a piece of America.
In doing that he gave Europe 20 years of peace ~ an unusual condition for them.
You should read that treaty some day.
Once it was promulgated, and commercial contacts re-established, the French began settling their assigned area, as did Scotland (it's called Nova Scotia these days, but it was also called Acadia back in the day ~ and included what is now hunks of New York, Maine, New Brunswick and Nova Scotia ~ fairly good sized territory which had bounds that'd not yet been surveyed).
A space between the highest peaks of the Eastern Cordillera (the Appalachians) and the Atlantic, between Carolana (later just Florida) in the South, and Nova Scotia in the North was set aside for OTHERS, not specifically England, but not exactly something the English couldn't go to.
There had already been settlements in the region ~ 30 of them to be exact, and only 3 have been studied to any extent.
That territory eventually became the core of the United States 173 years later.
The American people, however, came on the scene quite a bit earlier ~ and they came from throughout Europe, not just England. You can read the Booke of the Livinge and the Deade at any Virginia Room in a main library in any county in the Commonwealth and they are ALL LISTED. For my benefit they list those who were there BEFORE the division of the land ~ and even the Spanish had some records of those others who worked or them or, who were actually titled Spanish noblemen. Many of them stayed on in Virginia after Spain formally withdrew its protection from the territory.
Self government in the borning USA was a vital necessity. The climate was dreadful with recurring hurricanes, brutal winters, floods, tornados ~~~. Only the toughest of the tough, the best of all the best people could make it. And they did.
So, you are telling me America didn't start here not far from where I'm seated? America and its customs and traditions started WITH the Treaty of London 1604. This state has, in fact, a government that counts continuity all the way back to the bill of sale granted to The Virginia Company.
BTW, Spain didn't give England anything at all in that Treaty. And they specifically denied access to the Dutch (with whom they were still at war).
Do not be misled by popular histories.