Patently and demonstrably false.
Before the Confederacy attacked Fort Sumter, Confederate soldiers were already marching through Texas to seize the federal territory of New Mexico.
Source please.
The Confederacy wanted peace between itself and the Union - temporarily. The ultimate goal was to seize federal territory and populate it with slaveholders. That was the main reason why the South left in the first place.
To secede over not having slaveholder access to federal territory and then subsequently decide to completely abstain from entering that territory would have completely defeated the purpose of secession.
The Confederacy had already begun preparing for war before there even was a Confederacy as a corproate entity. The governor of Alabama publicly requested - and promptly received - the formation of volunteer companies external to the existing state militia in the fall of 1859.
Source please.
Don Alberts' book about Glorieta Pass.
And it stands to reason if you do the math: John R. Baylor began raising a regiment as soon as Texas seceded. His goal (which made excellent strategic sense) was to seize Mesilla in federal territory to prevent the Federals from surrounding Fort Bliss just inside the Texas border.
He took Mesilla on July 25, 1861 - 68 days after Sumter fell.
During that time he had raised a regiment in the San Antonio area and made his way in the heat of the South Texas spring and early summer 600 miles - stopping along the way to pick up recruits and horses and shore up Fort Bliss, etc.