Best example I can think of is in Star Wars Rebels, Season 1 Episode 1 (Droids in Distress), a barely trained (virtually untrained?)
Ezra does a Force push on Agent Kallus to save Zeb at the very end of the episode.
The first thing Kanan said to Ezra following that incident: Kanan: Your formal Jedi training starts tomorrow
This leads you to believe that Ezra has not had much, if any, Jedi training prior to this incident.
This is reinforced by some discussions earlier in the episode between Hera and Ezra in which he confides in her that he has not really received any training so far.
I don't have the exact quote handy, but I believe Ezra's response to her question about how his training is going is "What Jedi training".
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In The Phantom Menace, Qui-Gon indicates the only reason young Human Anakin can compete with alien pod racers who have better senses or more than two grasping limbs, is because of his innate Force use.
QUI-GON : He can see things before they happen.
That's why he appears to have such quick reflexes.
It is a Jedi trait.
And who says Rey has no Force training.
We don't know much about her past, but given the age she was left behind, the old Jedi Order would have already started her training.
And she could have picked some things up from all of the time Kylo used his own Telepathy on her.
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In the legends X-Wing series of books Corran Horn (without training in the force) uses non-vocal force persuasion to discourage a stormtrooper from finding him while he is hiding. http://starwars.wikia.com/wiki/X-Wing:_The_Krytos_Trap
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In The Clone Wars episode Children of the Force , there are newborns and small children that were already being found by the Jedi but not yet taken.
They could already levitate their toys.
Mind trick was not used there, but still though if one looks at Luke Skywalker even levitating things doesn't seem to be too easy (and I wouldn't count mind trick as advanced...
stopping blaster shots mid-air or deflecting them with the hand I would count as advanced).
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Entire population of planet
Haruun Kal 's population was described as force sensitive in Republic comics.
They are considered as "Legends" now I guess.
An example would be Kar Vastor .
Indigenous to Haruun Kal, learned about ways of the force by himself in a jungle, at least according to Legends.
He even managed to beat Mace Windu into unconsciousness once.
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If every Force-sensitive user needs a Force-sensitive master... ...who taught the first ever Force-sensitive master how to use the Force?
Logically speaking, at least one Force-sensitive individual has to have had the ability to use the Force without training or else no one would have been able to use the Force in the first place.
The Force is intuitive first; technical later.
Think back to Luke's initial training with Obi-Wan and the Marksman-H combat remote droid .
Kenobi didn't physically lead Luke through the "motions" of using the Force in order to blindly deflect the blaster bullets.
He didn't hold Luke's hands and say, "Swing like this ".
He provided simple verbal commands to guide Luke into connecting with his abilities-
it was up to Luke to discover what the Force actually felt like when tapped into and thus how to manipulate it.
As far as I'm concerned, Luke is an untrained Force user who does end up deflecting shots from the remote droid through use of the Force- just with a little encouragement from Obi-Wan.
Rey had more "training" in the art of the Force Mind Trick than Luke did when it came to Force Precognition .
Rey at least had the misfortune (but advantage) of seeing and experiencing Kylo Ren's Mind Probe which she intuitively was able to block by tapping into that specific area of the Force.
From there, she need only apply her newfound power at getting into the mind of someone else.
On the other hand, Luke was told to strap on a helmet, become blind, pick up a very complicated weapon, and then deflect small blaster bullets with the "edge" of said
complicated weapon- all without having the luxury of watching someone else do it or feel the ripple in the Force as another person performs the feat.
But then again, that's part of what makes Luke truly such a naturally powerful Force user.
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Before Luke met Yoda, he could do some basic telekinesis with no real force training.
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Another Legends Example:
In The Force Unleashed (Video Game)
Star Killer can already grab a lightsaber using telekinesis as a toddler.
Although it is not impossible he may have received training shortly after birth, it is very improbable.
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Young Asajj Ventress instinctively Force-pushes a Weequay raider away from herself in Clone Wars, "Nightsisters" (Episode 12).
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Kajin Savaros uses Force Push to actually disintegrate an Inquisitor on Coruscant.
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If I recall correctly, Han Solo's intuition, "I've got a bad feeling about this", was attributed to his being a force sensitive.
So completely untrained, he didn't even really believe in it at the time.
I believe the source for that was either the formerly cannon novels or one of the RPGs.
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In Star Wars The Force Awakens,     We see Rey, a seemingly untrained Force sensitive, use a Jedi mind trick with seemingly no training.   I have a friend who claims it would be impossible for any untrained Force-sensitive to use an "advanced maneuver"     like the mind trick.   Have we ever seen an untrained Force-sensitive individual use such a Force Power prior to The Force Awakens?  Canon is preferable, but Legends will work in addition to a canon answer.  Note:  Precognition or flying skills do not count as Force powers.
Have we ever seen an untrained Force-sensitive using Force powers?
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It would be only an assumption to say that Rey has not received any force training. Very little is stated about her backstory. However, there are in any case various examples of force-sensitives seemingly using the force having received little or no training. These examples include Corran Horn, Kar Vastor and even Luke Skywalker, depending on your definition of "training". There are many examples of innate use of the Force prior to awakening - such as the Clone Wars  episode  Children of the Force , where newborns and small children not yet taken by the Jedi can levitate toys.
Anakin is described as using innate Force power when out-competing alien pod racers in the Phantom Menace. It is also possible that Rey did have some training. Corran Horn in the X-Wing books uses non-vocal force persuasion to fool a stormtrooper when in hinding. In  The Clone Wars  episode  Children of the Force , newborns and small children not yet taken by the Jedi can levitate toys. Kar Vastor taught himself about the ways of the Force when living in a jungle, after which he even managed to beat Mace Windu. If all Force users needed a Master who could have trained the first Master? Various incidents from the training of Luke provide evidence of his innate ability to use the Force. Star Killer was able to grab a lightsaber even as a toddler. In Clone Wars Episode 12 Asajj Ventress instinctively Force-pushes a Weequay raider away. Kajin Savaros uses Force Push to actually disintegrate an Inquisitor on Coruscant. When Han Solo says "I've got a bad feeling about this", his intuition was attributed to his being a force sensitive even tho completely untrained.