My evidence is in the early minutes of Part Two of Ken Burns' documentary.
On TR's first day in the Executive Mansion, September 23 1901, he denied Xianity's promise of immortality when he gave tribute to his father:
What would I not give, if only he could have lived to see me here in the White House.
A theist TR would have known that his father was in heaven and was seeing him.
Right now that is my only evidence. Is there more?
Forgive me, but I think this is quite shaky evidence. He might have been saying it meaning that he wanted to experience his father's reaction to it. Notice that he says "if only he could have lived to see" not "if only he could have seen".
Inadequate evidence, yes.
I'm sure you will agree that "shaky" is ambiguous.
In the Catholic schools I attended, "heaven" is as real as anyplace on earth. Its denizens are alive and know what their offspring are doing.
A TR in those schools would not have said the words you suggest; he would have said "he sees me here in the White House."
Would TR have doubted?
If his parents had encouraged doubt, he would have. He also would have doubted that the fires of Catholicism's hell await doubters.
That's why I asked if there's more evidence.