According to this article you should have gotten it on your first use of the amiibo. And if you did not put Epona into a stable you may not get her to summon again. It does not seem that there are any requirements for getting her to summon other than using the amiibo and it being the first time doing so, there are no indicators that using it at a specific point in the game changes how this works.
If the player has the Smash Bros. Series Link Amiibo, you can use the
Amiibo Rune to tap Link onto the NFC reader. While most other Amiibo
will summon a supply drop of items - the first time the Smash. Bros
Series Link is used, Epona will be summoned instead.
So my guess is, based off their explanation, is that you potentially summoned her and didn't notice and it may be stuck where you can't summon her again. Or you summoned her in the Plateau and you did not get to put her in a stable, thus she disappears.
However, if you wish to keep and ride Epona - you must register the
horse at a stable as soon as possible. If you summon Epona in a place
where you cannot get to a Stable, like on the Great Plateau, you will
be unable to summon Epona again, as using the Smash. Bros Series Link
Amiibo on other days will only summon standard supply drop items.
However; there is another article that mentions a fountain that may be of help to you.
The downside, of course, is that if Epona dies -- that's it. You
cannot respawn Epona by tapping the amiibo again after she dies, and
you will only be able to get her by restarting your game or by finding
the Horse God's Great Fairy Fountain.
So perhaps there is a chance you can get Epona back, based off of what that article says:
Unlocking this Great Fairy will allow you to bring any horse back to
life -- provided that it was registered, and that you have the means
to pay for it. Even legendary or rare horses can be brought back to
life at this fountain -- including Epona (provided you already
summoned her with an amiibo).
But since it doesn't seem like you registered her if she did spawn by chance, it may not work either. The only solution remaining after that, as far as I can tell, is restarting, which I can't imagine you want to do.