There is nothing wrong with many constructions of only too:
✔ I'm only too happy to help you.
✔ They knew only too well that the bell meant playtime was over.
There is also nothing wrong with other words used in front of too good to be true:
✔ That was just too good to be true.
✔ That was simply too good to be true.
Both of these sound fine. The first arguably means something that has just crossed the line from believable to unbelievable. Although, in normal usage, it is actually just putting emphasis on something that is too good to be true.
But this sounds wrong to me:
? That was only too good to be true.
I don't see see how only can be used in this construction and make sense. To me, it has the same meaning as:
✘ That was solely too good to be true.
While this is technically grammatical, solely too good (as with only too good) is somewhat nonsensical—not least of all because it's not used idiomatically.
Possibly, you could interpret it as:
✔ On its own, that was too good to be true.
✔ Barring other considerations, that was too good to be true.
However, that would mean that you are reinterpreting the syntactic use of only, and changing it from an adverb (that modifies too) into an implied introductory clause. You'd be replacing what's actually written with something that isn't written at all.