I would imagine that you would actually be purchasing an option of buying ~~$1 trillion of stock in, say, a week or two. That would give them time to convert the $1 trillion bill into electronic money.
In theory you wouldn’t have to do that though. Trades settle in three days, so putting the tender up front should mean you are good to go. But I imagine that any transaction of this magnitude would involve a lot of phone calls. (“I have a customer here with a one trillion dollar bill”. ::click::)
If you did this with Vanguard, they would probably arrange to hold the money in some sort of holding account for a couple of weeks while they lined up sellers of shares. Ultimately, the Fed would hold most of the funds in the interim, with a commercial bank acting as the conduit. (Which brings us back to the CD scenario.)