Taylor Swift 's $100K donation has totally changed a cancer-stricken girl's life ... but, that young girl's mom says it came completely out of nowhere -- 'cause Taylor dropped the dough without ever reaching out to the fam.

We spoke with Katelynn Smoot , whose daughter Lilah was diagnosed with a rare and aggressive form of brain cancer earlier this year, about what the donation means to her and her family ... and, Smoot says it's given the family time to catch their collective breath.

Smoot says her husband was refreshing the GoFundMe one night and noticed the donation ... leaving the couple totally awestruck -- 'cause Taylor never reached out to inform them of the gift .

In fact, Swift still hasn't reached out ... it seems Taylor did something out of the goodness of her heart

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