"spontaneously happen" is a correct and usable phrase in written English.
It means something that occurs suddenly and without any planning or effort. Example: The flowers in the garden will spontaneously happen as the seeds were scattered by the wind.
Exact(3)
The assemble of separate DNA hairpin components can be triggered by specific target binding that are otherwise unable to spontaneously happen.
My hopes were that something awesome would just spontaneously happen that I could photograph and that would be it.
The same thing can spontaneously happen in humans, with the developing cell clusters from two separate fraternal twins combining and developing into a single person.
Similar(56)
This was meticulously planned, but for years it was branded as something that just spontaneously happened".
The increased glycolic acid could be possibly involved in the inhibition of vascular smooth muscle thickening that spontaneously happens in hypertensive rats [37].
But fur's resurgence, its transformation from fuddy-duddy to hip, did not happen spontaneously.
"This kind of thing doesn't happen spontaneously on this scale," he said.
The first step is for everyone to realize that it will not happen spontaneously.
The act of piercing requires little effort and may even happen spontaneously through corrosion.
Outside of natural disasters, few of history's momentous events happen spontaneously.
But it won't happen spontaneously, out of the "creative destruction" of local government that ministers apparently want.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com