Our first day at Disney was June 20th... I didn't even start trying to reserve FPs until about 2 weeks before. It took a couple of tries, not continual, and I got one for Mine Train. The FP was a good time on the 28th. I had to delete a day in between (they only let you reserve 7 days), but I got one for Mine Train.. I was ok with that.
Then, when we were there at Disney (at our Town home, not on property), at night I'd fiddle with my fps.. changing times, or even parks. We're not great planners and I truly dislike the new system. We have APs and we don't decide which park we want to go to too far in advance (but we did know we were going to MK on the 28th

). Days before the reservations I was able to get, not only several more FPs for Mine Train (which we reserved 2 more), but also A&E twice. I reserved A&E just because they were so hard to get. But then let them go because I know my daughter (17 yrs old) nor I were interested in seeing them.
Maybe the reason people can't get the reservations is because they choose other attractions and are trying to "fit" in the Mine Train. I always deleted the whole day, then choose Mine Train and the other two attractions. Whatever time I got Mine Train for, I would move the times of the other attractions around the Mine Train time.
I rarely got more than 2 times for Mine Train. But, one time that we took was for 10:15, the other for 3:30, so good times for us. We just scheduled that day for MK and fit stuff around it. The last time was for 7:10 which was fine for us, but we decided to do another park that day and let it go. Mine train is cute, and kinda fun for the VERY short time it lasts, but we did it twice and it was enough for us. It certainly isn't worth hours of waiting so I'm glad we so easily got the FPs.
So, no it's not a miracle at all. Just start practicing with the system now so you know how to use it. And use a computer, not the mobile apps. A computer makes it so easy to move to the next day (just click the arrow next to the day at the top) and then you can look down the list of the next day to see what's available.
Good Luck, Have fun!