1. The Elder Scrolls.
There are several of them on Nirn and some people have the ability to interpret them. And seeing as they are a veritable tapestry of fate, I'd say that Tiber Septims ascent to godliness would be recorded on them somewhere.
I'm aware that the Thalmor use the ban on Talos worship as a means to weaken the empire, but seeing as the Aldmarri Dominion are probably arrogant to believe their own BS, the Elder Scrolls would cause their reasoning for the White-Gold Concordat's Talos ban to lose any and all legitimacy.
The content of the Elder Scrolls are unknown to almost everyone on Nirn, and generally their contents are not shared with the public when they're deciphered.
2. The Talos Shrines
As many people know, those who pay at Aedra shrines receive a 'boon' from the gods. So the mere fact that a boon is received at a Talos shrine, the same as any other shrine, is proof of Talos' status.
So too can you get blessings from ancestral shrines and things of that nature. Just because you get a blessing or something doesn't necessarily mean the person that shrine is dedicated to is a god, merely that they are worshiped, which obviously, Talos is.
3. Martin Septim's ritual.
As many know, for Martin to open the gate to Mankar Camoran's paradise he required the blood of a Divine, and the blood of Tiber Septim, taken from a scraping of his old armor, worked.
Again, Martin's ritual is not public knowledge. The most anyone would ever know is part of the ritual was "blood of a divine."
4. Proof
Just as the Thalmor may claim that there is no proof that Talos is a god, they have no proof that he isn't other than a self-righteous notion that it's inconceivable for a human to be granted godhood before one of the mighty high elves.
The burden of proof is on those who would claim something exists. You can't prove a negative.
These aside, The Thalmor are obviously wrong in saying Talos is not a god, but as far as trying to convince the public of it, there's nothing really standing in their way (besides the public themselves, of course.)