the exact words
may be nowhere to be found, but the idea is quite plainly there.
If the founders didn't want a separation of church and state, they would have simply left it with a free exercise clause, and not included the establishment clause. But they did, because they didn't want a national religion. Which is not surprising since there were so many Christian sects, and at that time, many of them considered the other sects barely Christian.
Now, i will grant you, I'm not sure they founders were thinking separation of church and states, they were thinking separation of church and the feds. There were official state churches up until 1833. So clearly, they weren't envisioning it to apply to the states.
Of course, none of the BOR originally applied to the states. States could torture to gain confessions, or block 6th amendment rights, or do just about anything (and they often did). But selective incorporation fixed that, and now we apply it to the states as well.
Of course we have a ton of case law precedent going back to the 19th Century also establishing this.
Separation of Church and State is nothing more than TJ turn of phrase that succintly and accurately describes the relationship between religion in the form of an official church and the state. Which is you are not involved in our affairs and we are not involved yours.
That seems very clear in the 1st Amendment.