I have heard a few tricks of the trade on how to measure a foal and get a decent idea of how big they will be.
My 15.3 tb mare had her first pony foal this year. She has had 2 warmblood foals before this and one is just 5 and he is 16.2 and the other is a yearling same dad and is at least 15 hands and I am pretty sure he will be over 16.3. Dad was 17 hands.
The pony father is barely at 11 hands with no bigger size in his bloodlines.
So can I tell if the little guy will be a medium or large now, or do I just have to wait!?
I'm going to vote for you simply having to wait; but, I too think your foal is super duper cute. I have two yearlings that are by the same sire out of mares that are 14.1 and 13 hands. Both fillies are stair steps like their dams; however, what their height will be when fully mature is still a total unknown. They both already are taller than 13 hands. Sire is 15 hands.
Like all rules, there are exceptions. One of the smallest babies I ever had - truly tiny, like shetland pony baby sized - grew up to be 16.2h. He grew at a normal rate up to his yearling year and then totally took off.
Sure you could use the string test and there's at least 2 different ways to do it that different people will swear by; however, it's a guesstimate. When you are talking pony height an inch here or there makes a very big difference in price point, future potential (where and in what it can show), etc. You can do it (string test) until the cows come home but even when you talk about full siblings full grown on the ground, no two are identical and then when you add the crap shoot of a horse x pony combination genetics can make a liar out of you every time The string test may guide you as to whether or not you have a medium or a large but it's not a guarantee and I've seen more than a few surprises with a first time cross.