This is not the same situation and the word "not" is not optional here. It was "omitted" on purpose.

Student or Learner
"The world's needs grow greater every day and God is opening many doors of opportunity here at home and around the globe. However, only with your support can [Subject] respond to these hurting people."
We don’t have the adverb not before the focusing word only. So, Why did the subject and verb get reversed? Is the word not optional? I came across a lot of texts where the word also can be omitted. (Not only…., but … ) without also.
P.S.: I have concealed name intentionally. It might be used for advertisement.
This is not the same situation and the word "not" is not optional here. It was "omitted" on purpose.
'Only when' can be interpreted as ' 'on no occasions except when'.
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