How do you prove a negative? Along with prohibiting the establishment of a religion the 1st Amendment prohibits the making of any law that impedes the free exercise of religion. The bigoted left got around the "making" part of the Constitution by finding a loophole that did not exist. The modern concept of "separation church/state" is an invention by a FDR appointed Supreme Court justice who was also a former KKK member who hated Papists. The bigoted left drags out Jefferson letters that tend to reinforce the separation concept but Jefferson's letters are not part of Constitutional law.
There wasn't Jefferson's "letters" there was Jefferson't letter to the Danbury Baptists who wrote inquiring as to whether their Church would be allowed to exist. Jefferson wrote back assuring them that government would not interfere with worship as there was a separation between church and state.
The letter in question.
Gentlemen
The affectionate sentiments of esteem and approbation which you are so good as to express towards me, on behalf of the Danbury Baptist association, give me the highest satisfaction. my duties dictate a faithful and zealous pursuit of the interests of my constituents, & in proportion as they are persuaded of my fidelity to those duties, the discharge of them becomes more and more pleasing.
Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should "make no law respecting an establishment of religion,
or prohibiting the free exercise thereof," thus building a wall of separation between Church & State. Adhering to this expression of the supreme will of the nation in behalf of the rights of conscience, I shall see with sincere satisfaction the progress of those sentiments which tend to restore to man all his natural rights, convinced he has no natural right in opposition to his social duties.
I reciprocate your kind prayers for the protection & blessing of the common father and creator of man, and tender you for yourselves & your religious association, assurances of my high respect & esteem.
Th Jefferson
Jan. 1. 1802.