Thanks for your question.
I am afraid that the bad news is that if the child is not yours and there is nothing else tying your girlfriend to the UK, it is highly unlikely that any application she makes to teh Home Office for Settlement in the Uk will be refused.
The best thing she could do is for her to return to her home country, you to travel out there and get married and then for her and teh child to make an application for a Spouse and Dependants Visa respectively. If the child is a UK Citizen, she will only need to make an application for herfself.
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