Americans in search of cheap land illegally immigrated to Mexican Texas, rebelled against the government, declared independence, and won. Lacking the men and resources to protect themselves against the Indians and Mexicans, they then asked to be annexed in the US, and got what they wanted. The American government then provoked a war with Mexico over the location of the new border, won it, and gained control of several states, including California, in the process. Would any of this have happened if the Revolution had failed?
The illegal immigration part was inevitable, but the rest was not. Great Britain would have had zero interest in provoking a war with Mexico. Large parts of what is now the US might still be included in Mexico today but for the success of the Revolution.