I would say manifest destiny was born with the Louisiana purchase. I don't think many US Americans dreamed of expanding beyond the Mississippi until they woke up one day and read in the newspapers that the US had just doubled in size. At that point, the gov't was looking at the Northwest as the window to the Pacific. Everyday folk had to first fill up the territories east of the Miss. They did settle the west bank, but as you said, it wasn't til after the M-A war that westward settlement really got going.
In an ATL where Spain holds on to Louisiana, by the time the US fills up, Spain has firm control of the west bank. The call may very well be "Go west, young man, and become Spanish", or the alternative "Move to the city, young man, and get a job"
I think it is true that the US government at the time wasn't deadset on expanding west, but I keep reading stories about how the farmers themselves would create a village, have plenty of kids and the next generation would just move west for new land.
And that the expanding US population would keep pushing west and nobody could prevent them from crossing the Mississippi and building their settlements there too.
But still even if they do move perhaps they could be integrated into the Spanish/French colony rather than taking it over. Especially if their numbers are lower than they'd be if the US actuslly annexed the area.
Now what I'm interested in is, would Spain be able to populate these territories itself and perhaps attract other European immigrants especially Catholic ones like the Irish or the Italians instead of the US?