The primary evidence for ogham is a few hundred inscribed stones, most of them in Ireland and a smaller number in Wales, Scotland, the Isle of Man and Cornwall, cut broadly between the fourth and the seventh centuries. Their contents are unromantic. Almost all of them record a personal name, usually in the genitive and often with a father's or a kindred's name attached, in the manner of a boundary or memorial marker. Nothing on them is divinatory.
The learned tradition about the letters is later and is written rather than carved. Medieval Irish scholars compiled lists of kennings for the letter names, and the grammatical tract known as the Auraicept na nEces sets out much of what is known about how the alphabet was understood by literate Christians several centuries after the stones were cut. Some letter names are tree names and some are not, and the strength of the association has been debated by philologists since.
The tree calendar familiar from modern books is a different matter again. Robert Graves set it out in The White Goddess in 1948 as a recovered druidic system of thirteen months, and he built it himself, working from the medieval letter lists and his own poetic reasoning. Scholars of early Irish rejected it immediately and have gone on rejecting it.
Divinatory ogham is therefore a twentieth-century construction on a genuinely ancient script, and the script's own attested use was to write names on stone.