The old Jedi Order took students from infancy in order to control their emotional attachments, which they saw as gateways to the dark side. This is why they were so reluctant to take on Anakin as a Jedi. I think it gave the wrong impression that learning how to use the Force took years, when that really isn’t the entirely the case. It has more to do with belief, and one’s ability to “let go of your conscious self”.
It also surprises me a little that people haven’t considered as much that the Force itself has changed between the trilogies. The Force isn’t a static ability, it’s dynamic and connected to life itself, making it in a way alive.
Episode 7 is literally called The Force Awakens. What does that mean? Is it not possible that this awakening is not partially responsible for the feats we’ve seen across the board in the new films, like Kylo Ren freezing blaster bolts, Rey’s fast-growing abilities, their subsequent Force-Skype sessions, Leia pulling herself back to the ship, Luke’s Force projection, even broom boy’s subtle Force pull?
You could even argue this began with Luke in the OT, the first real student of the Force since the Jedi Purge. He really only had a few weeks at most of official training with Yoda, but in Return of the Jedi, only a year later with no additional training under Yoda, he is on the verge of officially becoming a Jedi.
It raises some questions about the nature of the Force. Does the overall use of the Force have an affect on its potential in existing Force-users? Does the Force have a will of its own to choose who it acts through? Did training Jedi from infancy have a side-effect of limiting their relationship with the Force in ways that didn’t exist for those who discovered it at adulthood? Is the Force just like an ocean, where the tide can rise and fall?
I personally think these questions about the Force should really never be answered fully, and should remain mysterious, simple-yet-complicated, and sometimes contradictory, much like the Tao that inspired it, and also as a concept of a universal religion-symbol that George meant it to be, since religions are also endlessly debated upon.
I think the important theme we are meant to take from the Force is the ideas of faith and belief, the crux of all religions, and the internal power we can get from faith in our own lives, religious or not. Luke struggles with the Force in the OT because of his doubt in the Force and his own personal self-doubt.
Rey on the other hand grew up with the legend of Luke Skywalker and the Jedi, and not long after learning about the reality of the them, she slowly learns that she’s also connected to this Force and begins her own journey of self-discovery and self-actualization.
With broom boy, moments before his Force use, he is being told the story of Luke Skywalker’s grand stand against the evil First Order, with wonder in his eyes. He believes in the Jedi, in the Force, and that subtle moment, something he might not have even realized he did, is a representation of what the power of faith and hope can have in the world and in ourselves.
Anyway, just my two cents. Not trying to argue, just sharing my perspective.