So far we've seen 3 saiyans from universe 6 with an important role in Dragon Ball Super. In a short period of time, less than 48 hours for Kale and Caulifla if I recall correctly, and less than a year for Kyabe, they've mastered more than one transformation. Kale mastered super saiyan berserker and super saiyan green, Caulifla mastered super saiyan , ultra super saiyan (not sure if this is a state or transformation) which chances to master super saiyan 3 in the tournament according to Goku, and Kyabe mastered super saiyan and super saiyan . Why is so? Do universe 6 saiyans transform naturaly more easily than universe 7 saiyans or is there another reason?
Officially the original super saiyan transformation was triggered by pure anger and enough raw power to transform. The only possible explanation this is that U6 saiyan have the power but they are not that interested in fighting so they never really explored their power.
One more thing that you can't expect a story to be perfect and with no plot armor because the mangaka has to make the story interesting.
The answer to this is more complicated than it seems. Because the answer is yes and no at the same time. Due to proper guidance they were able to achieve higher forms easier but they simply "unlocked" it they didn't master it. As shown in episode 114 Goku has mastered the movements and can withstand 2 saiyans on his own in a lower form if he wants. They are able to have a higher power output but in terms of effieciency they lack a lot.
Unlocking the Saiyan state(s) require strong emotions and pushing yourself to the utter limit. Kyabe's anger unlocked ssj1, his desire to show his master around on his planet in his universe unlocked ssj2. Due to the high stress levels caused by the punishment for losing the tournament their emotions are affected majorily resulting in an easier way to unlock states if used properly.
The girls had similar experiences, one desire strength and power while the other desires to protect her sister and to fight beside her.
Goku unlocked his states when he was pushed to his limits with the desire of becoming stronger. Gohan had the desire for justice and Vegeta the desire as his duty as the Saiyan prince and ofcourse his jealousy towards Kakarot.
But I only want to emphasize on the difference between unlocking a new saiyan state AND mastering a new saiyan state. SSJ2 has more raw power than SSJ1. A mastered SSJ1 is stronger than SSJ2 due to knowing the limits and how to use his body with the stamina output etc.
I hope this answers your question. Feel free to comment if you would like to know more.
PS: if I dive into it I can provide all episodes to back up my statements but that would require a lot time. If you wish I can provide a list of episodes but I don't think it is needed for this question.